Daily Papers

Existing Large Reasoning Models (LRMs) have shown the potential of reinforcement learning (RL) to enhance the complex reasoning capabilities of Large Language Models~(LLMs). While they achieve remarkable performance on challenging tasks such as mathematics and coding, they often rely on their internal knowledge to solve problems, which can be inadequate for time-sensitive or knowledge-intensive questions, leading to inaccuracies and hallucinations. To address this, we propose R1-Searcher, a novel two-stage outcome-based RL approach designed to enhance the search capabilities of LLMs. This method allows LLMs to autonomously invoke external search systems to access additional knowledge during the reasoning process. Our framework relies exclusively on RL, without requiring process rewards or distillation for a cold start. % effectively generalizing to out-of-domain datasets and supporting both Base and Instruct models. Our experiments demonstrate that our method significantly outperforms previous strong RAG methods, even when compared to the closed-source GPT-4o-mini.

In this paper, we propose R^3: Learning Reasoning through Reverse Curriculum Reinforcement Learning (RL), a novel method that employs only outcome supervision to achieve the benefits of process supervision for large language models. The core challenge in applying RL to complex reasoning is to identify a sequence of actions that result in positive rewards and provide appropriate supervision for optimization. Outcome supervision provides sparse rewards for final results without identifying error locations, whereas process supervision offers step-wise rewards but requires extensive manual annotation. R^3 overcomes these limitations by learning from correct demonstrations. Specifically, R^3 progressively slides the start state of reasoning from a demonstration's end to its beginning, facilitating easier model exploration at all stages. Thus, R^3 establishes a step-wise curriculum, allowing outcome supervision to offer step-level signals and precisely pinpoint errors. Using Llama2-7B, our method surpasses RL baseline on eight reasoning tasks by 4.1 points on average. Notebaly, in program-based reasoning on GSM8K, it exceeds the baseline by 4.2 points across three backbone models, and without any extra data, Codellama-7B + R^3 performs comparable to larger models or closed-source models.

Reward models have been increasingly critical for improving the reasoning capability of LLMs. Existing research has shown that a well-trained reward model can substantially improve model performances at inference time via search. However, the potential of reward models during RL training time still remains largely under-explored. It is currently unclear whether these reward models can provide additional training signals to enhance the reasoning capabilities of LLMs in RL training that uses sparse success rewards, which verify the correctness of solutions. In this work, we evaluate popular reward models for RL training, including the Outcome-supervised Reward Model (ORM) and the Process-supervised Reward Model (PRM), and train a collection of LLMs for math problems using RL by combining these learned rewards with success rewards. Surprisingly, even though these learned reward models have strong inference-time performances, they may NOT help or even hurt RL training, producing worse performances than LLMs trained with the success reward only. Our analysis reveals that an LLM can receive high rewards from some of these reward models by repeating correct but unnecessary reasoning steps, leading to a severe reward hacking issue. Therefore, we introduce two novel reward refinement techniques, including Clipping and Delta. The key idea is to ensure the accumulative reward of any reasoning trajectory is upper-bounded to keep a learned reward model effective without being exploited. We evaluate our techniques with multiple reward models over a set of 1.5B and 7B LLMs on MATH and GSM8K benchmarks and demonstrate that with a carefully designed reward function, RL training without any additional supervised tuning can improve all the evaluated LLMs, including the state-of-the-art 7B LLM Qwen2.5-Math-7B-Instruct on MATH and GSM8K benchmarks.

Reinforcement Learning (RL) has emerged as a transformative approach for aligning and enhancing Large Language Models (LLMs), addressing critical challenges in instruction following, ethical alignment, and reasoning capabilities. This survey offers a comprehensive foundation on the integration of RL with language models, highlighting prominent algorithms such as Proximal Policy Optimization (PPO), Q-Learning, and Actor-Critic methods. Additionally, it provides an extensive technical overview of RL techniques specifically tailored for LLMs, including foundational methods like Reinforcement Learning from Human Feedback (RLHF) and AI Feedback (RLAIF), as well as advanced strategies such as Direct Preference Optimization (DPO) and Group Relative Policy Optimization (GRPO). We systematically analyze their applications across domains, i.e., from code generation to tool-augmented reasoning. We also present a comparative taxonomy based on reward modeling, feedback mechanisms, and optimization strategies. Our evaluation highlights key trends. RLHF remains dominant for alignment, and outcome-based RL such as RLVR significantly improves stepwise reasoning. However, persistent challenges such as reward hacking, computational costs, and scalable feedback collection underscore the need for continued innovation. We further discuss emerging directions, including hybrid RL algorithms, verifier-guided training, and multi-objective alignment frameworks. This survey serves as a roadmap for researchers advancing RL-driven LLM development, balancing capability enhancement with safety and scalability.

Large Language Models (LLMs) increasingly rely on external tools such as search engines to solve complex agentic tasks that require reasoning and external knowledge retrieval. Recently, reinforcement learning with verifiable rewards (RLVR) has demonstrated its effectiveness in advancing capabilities of LLMs by rewarding the final answers via outcome rewards. While straightforward to supervise, outcome rewards only provide sparse signals and delayed feedback, which limits their effectiveness on long trajectories. Process rewards address this by evaluating intermediate steps, providing fine-grained supervision and encouraging grounded problem solving. However, it is notoriously hard to annotate step-wise labels, especially in non-verifiable process without "golden" answers. Furthermore, step-wise judgment requires the balance between local quality with contribution to the final outcome, as optimizing towards higher process reward may not always align with better final outcomes. To address the above challenges, we introduce Principle Process Reward (PPR), an RL approach that unifies principled step-level assessment and outcome verification. We train a principle-based reward model to improve the transparency and reliability of process evaluation, and further introduce a Reward Normalization (ReNorm) strategy to calibrate outcome and process rewards. Experiment results show that PPR achieves state-of-the-art performance across a wide range of benchmarks, demonstrating its impressive robustness and generalization. Our code and model collection is available in this link.

Training critiquing language models to assess and provide feedback on model outputs is a promising way to improve LLMs for complex reasoning tasks. However, existing approaches typically rely on stronger supervisors for annotating critique data. To address this, we propose Critique-RL, an online RL approach for developing critiquing language models without stronger supervision. Our approach operates on a two-player paradigm: the actor generates a response, the critic provides feedback, and the actor refines the response accordingly. We first reveal that relying solely on indirect reward signals from the actor's outputs for RL optimization often leads to unsatisfactory critics: while their helpfulness (i.e., providing constructive feedback) improves, the discriminability (i.e., determining whether a response is high-quality or not) remains poor, resulting in marginal performance gains. To overcome this, Critique-RL adopts a two-stage optimization strategy. In stage I, it reinforces the discriminability of the critic with direct rule-based reward signals; in stage II, it introduces indirect rewards based on actor refinement to improve the critic's helpfulness, while maintaining its discriminability via appropriate regularization. Extensive experiments across various tasks and models show that Critique-RL delivers substantial performance improvements. For example, it achieves a 9.02% gain on in-domain tasks and a 5.70% gain on out-of-domain tasks for Qwen2.5-7B, highlighting its potential.

Reinforcement learning with verifiable rewards (RLVR) has emerged to be a predominant paradigm for mathematical reasoning tasks, offering stable improvements in reasoning ability. However, Outcome Reward Models (ORMs) in RLVR are too coarse-grained to distinguish flawed reasoning within correct answers or valid reasoning within incorrect answers. This lack of granularity introduces noisy and misleading gradients significantly and hinders further progress in reasoning process quality. While Process Reward Models (PRMs) offer fine-grained guidance for intermediate steps, they frequently suffer from inaccuracies and are susceptible to reward hacking. To resolve this dilemma, we introduce PRocess cOnsistency Filter (PROF), an effective data process curation method that harmonizes noisy, fine-grained process rewards with accurate, coarse-grained outcome rewards. Rather than naively blending PRM and ORM in the objective function (arXiv:archive/2506.18896), PROF leverages their complementary strengths through consistency-driven sample selection. Our approach retains correct responses with higher averaged process values and incorrect responses with lower averaged process values, while maintaining positive/negative training sample balance. Extensive experiments demonstrate that our method not only consistently improves the final accuracy over 4% compared to the blending approaches, but also strengthens the quality of intermediate reasoning steps. Codes and training recipes are available at https://github.com/Chenluye99/PROF.

Large language models (LLMs) increasingly rely on thinking models that externalize intermediate steps and allocate extra test-time compute, with think-twice strategies showing that a deliberate second pass can elicit stronger reasoning. In contrast, most reward models (RMs) still compress many quality dimensions into a single scalar in one shot, a design that induces judgment diffusion: attention spreads across evaluation criteria, yielding diluted focus and shallow analysis. We introduce branch-and-rethink (BR-RM), a two-turn RM that transfers the think-twice principle to reward modeling. Turn 1 performs adaptive branching, selecting a small set of instance-critical dimensions (such as factuality and safety) and sketching concise, evidence-seeking hypotheses. Turn 2 executes branch-conditioned rethinking, a targeted reread that tests those hypotheses and scrutinizes only what matters most. We train with GRPO-style reinforcement learning over structured two-turn traces using a simple binary outcome reward with strict format checks, making the approach compatible with standard RLHF pipelines. By converting all-at-oncescoringintofocused, second-lookreasoning, BR-RMreducesjudgmentdiffusionandimproves sensitivity to subtle yet consequential errors while remaining practical and scalable. Experimental results demonstrate that our model achieves state-of-the-art performance on three challenging reward modeling benchmarks across diverse domains. The code and the model will be released soon.

Reinforcement learning (RL) for continuous control often requires large amounts of online interaction data. Value-based RL methods can mitigate this burden by offering relatively high sample efficiency. Some studies further enhance sample efficiency by incorporating offline demonstration data to "kick-start" training, achieving promising results in continuous control. However, they typically compute the Q-function independently for each action dimension, neglecting interdependencies and making it harder to identify optimal actions when learning from suboptimal data, such as non-expert demonstration and online-collected data during the training process. To address these issues, we propose Auto-Regressive Soft Q-learning (ARSQ), a value-based RL algorithm that models Q-values in a coarse-to-fine, auto-regressive manner. First, ARSQ decomposes the continuous action space into discrete spaces in a coarse-to-fine hierarchy, enhancing sample efficiency for fine-grained continuous control tasks. Next, it auto-regressively predicts dimensional action advantages within each decision step, enabling more effective decision-making in continuous control tasks. We evaluate ARSQ on two continuous control benchmarks, RLBench and D4RL, integrating demonstration data into online training. On D4RL, which includes non-expert demonstrations, ARSQ achieves an average 1.62times performance improvement over SOTA value-based baseline. On RLBench, which incorporates expert demonstrations, ARSQ surpasses various baselines, demonstrating its effectiveness in learning from suboptimal online-collected data. Project page is at https://sites.google.com/view/ar-soft-q

Large Language Models (LLMs) are powerful but prone to hallucinations due to static knowledge. Retrieval-Augmented Generation (RAG) helps by injecting external information, but current methods often are costly, generalize poorly, or ignore the internal knowledge of the model. In this paper, we introduce R1-Searcher++, a novel framework designed to train LLMs to adaptively leverage both internal and external knowledge sources. R1-Searcher++ employs a two-stage training strategy: an initial SFT Cold-start phase for preliminary format learning, followed by RL for Dynamic Knowledge Acquisition. The RL stage uses outcome-supervision to encourage exploration, incorporates a reward mechanism for internal knowledge utilization, and integrates a memorization mechanism to continuously assimilate retrieved information, thereby enriching the model's internal knowledge. By leveraging internal knowledge and external search engine, the model continuously improves its capabilities, enabling efficient retrieval-augmented reasoning. Our experiments demonstrate that R1-Searcher++ outperforms previous RAG and reasoning methods and achieves efficient retrieval. The code is available at https://github.com/RUCAIBox/R1-Searcher-plus.

Different from its counterpart outcome reward models (ORMs), which evaluate the entire responses, a process reward model (PRM) scores a reasoning trajectory step by step, providing denser and more fine grained rewards. However, training a PRM requires labels annotated at every intermediate step, presenting significant challenges for both manual and automatic data collection. This paper aims to address this challenge. Both theoretically and empirically, we show that an implicit PRM can be obtained at no additional cost, by simply training an ORM on the cheaper response-level labels. The only assumption is to parameterize the outcome reward as the log-likelihood ratios of the policy and reference models, which can be optimized regardless of the specific choice of loss objectives. In experiments, we instantiate our implicit PRMs with various objectives and evaluate their performance on MATH. We show that our implicit PRM outperforms a strong MCTS-based baseline \'a la Math-Shepherd using less than 1/38 of the training data. Its performance can be further improved with majority voting. We further find that scaling up instructions and responses benefits our implicit PRM, and the latter brings a larger gain. Particularly, we find that our implicit PRM, when instantiated with the cross-entropy (CE) loss, is more data-efficient and can keep improving generation models even when trained with only one response per instruction, the setup that suffers from extreme data scarcity and imbalance. Further, instructions should be relevant to downstream tasks while the diversity of responses does not bring gains. Surprisingly, training on extra Math-Shepherd step labels brings no further improvements to our implicit PRM trained on only outcome data. We hope that our work will encourage a rethinking of PRM training approaches and contribute to making training PRMs more accessible.

Large language model (LLM)-based agents are increasingly trained with reinforcement learning (RL) to enhance their ability to interact with external environments through tool use, particularly in search-based settings that require multi-turn reasoning and knowledge acquisition. However, existing approaches typically rely on outcome-based rewards that are only provided at the final answer. This reward sparsity becomes particularly problematic in multi-turn settings, where long trajectories exacerbate two critical issues: (i) advantage collapse, where all rollouts receive identical rewards and provide no useful learning signals, and (ii) lack of fine-grained credit assignment, where dependencies between turns are obscured, especially in long-horizon tasks. In this paper, we propose Information Gain-based Policy Optimization (IGPO), a simple yet effective RL framework that provides dense and intrinsic supervision for multi-turn agent training. IGPO models each interaction turn as an incremental process of acquiring information about the ground truth, and defines turn-level rewards as the marginal increase in the policy's probability of producing the correct answer. Unlike prior process-level reward approaches that depend on external reward models or costly Monte Carlo estimation, IGPO derives intrinsic rewards directly from the model's own belief updates. These intrinsic turn-level rewards are combined with outcome-level supervision to form dense reward trajectories. Extensive experiments on both in-domain and out-of-domain benchmarks demonstrate that IGPO consistently outperforms strong baselines in multi-turn scenarios, achieving higher accuracy and improved sample efficiency.

Recent Large Language Model (LLM) post-training methods rely on token-level clipping mechanisms during Reinforcement Learning (RL). However, we identify a fundamental flaw in this Outcome-Supervised RL (OSRL) paradigm: the Importance Sampling (IS) ratios of positive-advantage tokens are mismatched, leading to unbalanced token weighting for positive and negative tokens. This mismatch suppresses the update of low-probability tokens while over-amplifying already high-probability ones. To address this, we propose Asymmetric Importance Sampling Policy Optimization (ASPO), which uses a simple yet effective strategy that flips the IS ratios of positive-advantage tokens, aligning their update direction with the learning dynamics of negative ones. AIS further incorporates a soft dual-clipping mechanism to stabilize extreme updates while maintaining gradient flow. Comprehensive experiments on coding and mathematical reasoning benchmarks demonstrate that ASPO significantly mitigates premature convergence, improves training stability, and enhances final performance over strong GRPO-based baselines. Our analysis provides new insights into the role of token-level weighting in OSRL and highlights the critical importance of correcting IS in LLM RL. The code and models of ASPO are available at https://github.com/wizard-III/Archer2.0.

Reinforcement learning (RL) has proven effective in incentivizing the reasoning abilities of large language models (LLMs), but suffers from severe efficiency challenges due to its trial-and-error nature. While the common practice employs supervised fine-tuning (SFT) as a warm-up stage for RL, this decoupled two-stage approach limits interaction between SFT and RL, thereby constraining overall effectiveness. This study introduces a novel method for learning reasoning models that employs bilevel optimization to facilitate better cooperation between these training paradigms. By conditioning the SFT objective on the optimal RL policy, our approach enables SFT to meta-learn how to guide RL's optimization process. During training, the lower level performs RL updates while simultaneously receiving SFT supervision, and the upper level explicitly maximizes the cooperative gain-the performance advantage of joint SFT-RL training over RL alone. Empirical evaluations on five reasoning benchmarks demonstrate that our method consistently outperforms baselines and achieves a better balance between effectiveness and efficiency.

Recent advances in Reinforcement Learning with Verified Reward (RLVR) have driven the emergence of more sophisticated cognitive behaviors in large language models (LLMs), thereby enhancing their reasoning capabilities. However, in prior RLVR pipelines, the repeated use of static initial-state sampling drawn exactly from the dataset distribution during each sampling phase produced overly deterministic, low diversity model behavior, which manifested as rapid entropy collapse and hindered sustained performance gains during prolonged training. To address this issue, we introduce CURE (Critical-token-gUided Re concatenation for Entropy-collapse prevention), a two-stage framework that balances exploration and exploitation. Specifically, in the first stage, to deliberately steer the model toward novel yet coherent contexts, we re-generate at high-entropy critical tokens and jointly optimize the original and the branched trajectories. The further comparison with vanilla DAPO shows that the regeneration process achieves a better performance on math reasoning tasks while sustaining a high-level entropy degree for exploration. In the second stage, we continue training with static initial-state sampling by DAPO, intentionally placing the model in a familiar state to gradually strengthen exploitation. Extensive experiments on Qwen-2.5-Math-7B show that, compared to other RLVR methods, CURE achieves a 5% performance gain across six math benchmarks, establishing state-of-the-art performance in both entropy and accuracy. A series of experiments further validate the effectiveness of our approach. Code is available at https://github.com/bytedance/CURE.

Large reasoning models (LRMs) have recently shown promise in solving complex math problems when optimized with Reinforcement Learning (RL). But conventional approaches rely on outcome-only rewards that provide sparse feedback, resulting in inefficient optimization process. In this work, we investigate the function of process reward models (PRMs) to accelerate the RL training for LRMs. We propose a novel intrinsic signal-driven generative process evaluation mechanism operating at the thought level to address major bottlenecks in RL-based training. Specifically, instead of requiring PRMs to know how to solve problems, our method uses intrinsic signals in solutions to judge stepwise correctness and aggregate contiguous correct/incorrect steps into coherent 'thought' units. This structured, thought-level rewards enable more reliable credit assignment by reducing ambiguity in step segmentation and alleviating reward hacking. We further introduce a capability-adaptive reward mechanism that dynamically balances exploration and exploitation based on the LRM's current proficiency, guiding learning without stifling creative trial-and-error. These innovations are integrated into a new off-policy RL algorithm, TP-GRPO, which extends grouped proximal optimization with process-based rewards and improves training efficiency. Experiments on 1.5B and 7B parameter LRMs demonstrate that our method achieves higher problem-solving accuracy with significantly fewer training samples than outcome-only reward baselines. The results validate that well-structured process rewards can substantially accelerate LRM optimization in math reasoning tasks. Code is available at https://github.com/cs-holder/tp_grpo.

LLM-based (Large Language Model) GUI (Graphical User Interface) agents can potentially reshape our daily lives significantly. However, current LLM-based GUI agents suffer from the scarcity of high-quality training data owing to the difficulties of trajectory collection and reward annotation. Existing works have been exploring LLMs to collect trajectories for imitation learning or to offer reward signals for online RL training. However, the Outcome Reward Model (ORM) used in existing works cannot provide finegrained feedback and can over-penalize the valuable steps in finally failed trajectories. To this end, we propose Progress Reward Model (ProgRM) to provide dense informative intermediate rewards by predicting a task completion progress for each step in online training. To handle the challenge of progress reward label annotation, we further design an efficient LCS-based (Longest Common Subsequence) self-annotation algorithm to discover the key steps in trajectories and assign progress labels accordingly. ProgRM is evaluated with extensive experiments and analyses. Actors trained with ProgRM outperform leading proprietary LLMs and ORM-trained actors, illustrating the effectiveness of ProgRM. The codes for experiments will be made publicly available upon acceptance.

Reinforcement learning for LLM reasoning has rapidly emerged as a prominent research area, marked by a significant surge in related studies on both algorithmic innovations and practical applications. Despite this progress, several critical challenges remain, including the absence of standardized guidelines for employing RL techniques and a fragmented understanding of their underlying mechanisms. Additionally, inconsistent experimental settings, variations in training data, and differences in model initialization have led to conflicting conclusions, obscuring the key characteristics of these techniques and creating confusion among practitioners when selecting appropriate techniques. This paper systematically reviews widely adopted RL techniques through rigorous reproductions and isolated evaluations within a unified open-source framework. We analyze the internal mechanisms, applicable scenarios, and core principles of each technique through fine-grained experiments, including datasets of varying difficulty, model sizes, and architectures. Based on these insights, we present clear guidelines for selecting RL techniques tailored to specific setups, and provide a reliable roadmap for practitioners navigating the RL for the LLM domain. Finally, we reveal that a minimalist combination of two techniques can unlock the learning capability of critic-free policies using vanilla PPO loss. The results demonstrate that our simple combination consistently improves performance, surpassing strategies like GRPO and DAPO.

Reinforcement Learning (RL) has shown remarkable success in enhancing the reasoning capabilities of Large Language Models (LLMs). Process-Supervised RL (PSRL) has emerged as a more effective paradigm compared to outcome-based RL. However, existing PSRL approaches suffer from limited exploration efficiency, both in terms of branching positions and sampling. In this paper, we introduce a novel PSRL framework (AttnRL), which enables efficient exploration for reasoning models. Motivated by preliminary observations that steps exhibiting high attention scores correlate with reasoning behaviors, we propose to branch from positions with high values. Furthermore, we develop an adaptive sampling strategy that accounts for problem difficulty and historical batch size, ensuring that the whole training batch maintains non-zero advantage values. To further improve sampling efficiency, we design a one-step off-policy training pipeline for PSRL. Extensive experiments on multiple challenging mathematical reasoning benchmarks demonstrate that our method consistently outperforms prior approaches in terms of performance and sampling and training efficiency.

A broad use case of large language models (LLMs) is in goal-directed decision-making tasks (or "agent" tasks), where an LLM needs to not just generate completions for a given prompt, but rather make intelligent decisions over a multi-turn interaction to accomplish a task (e.g., when interacting with the web, using tools, or providing customer support). Reinforcement learning (RL) provides a general paradigm to address such agent tasks, but current RL methods for LLMs largely focus on optimizing single-turn rewards. By construction, most single-turn RL methods cannot endow LLMs with the ability to intelligently seek information over multiple turns, perform credit assignment, or reason about their past actions -- all of which are critical in agent tasks. This raises the question: how can we design effective and efficient multi-turn RL algorithms for LLMs? In this paper, we develop a framework for building multi-turn RL algorithms for fine-tuning LLMs, that preserves the flexibility of existing single-turn RL methods for LLMs (e.g., proximal policy optimization), while accommodating multiple turns, long horizons, and delayed rewards effectively. To do this, our framework adopts a hierarchical RL approach and runs two RL algorithms in parallel: a high-level off-policy value-based RL algorithm to aggregate reward over utterances, and a low-level RL algorithm that utilizes this high-level value function to train a token policy within each utterance or turn. Our hierarchical framework, Actor-Critic Framework with a Hierarchical Structure (ArCHer), can also give rise to other RL methods. Empirically, we find that ArCHer significantly improves efficiency and performance on agent tasks, attaining a sample efficiency of about 100x over existing methods, while also improving with larger model capacity (upto the 7 billion scale that we tested on).

A growing trend for value-based reinforcement learning (RL) algorithms is to capture more information than scalar value functions in the value network. One of the most well-known methods in this branch is distributional RL, which models return distribution instead of scalar value. In another line of work, hybrid reward architectures (HRA) in RL have studied to model source-specific value functions for each source of reward, which is also shown to be beneficial in performance. To fully inherit the benefits of distributional RL and hybrid reward architectures, we introduce Multi-Dimensional Distributional DQN (MD3QN), which extends distributional RL to model the joint return distribution from multiple reward sources. As a by-product of joint distribution modeling, MD3QN can capture not only the randomness in returns for each source of reward, but also the rich reward correlation between the randomness of different sources. We prove the convergence for the joint distributional Bellman operator and build our empirical algorithm by minimizing the Maximum Mean Discrepancy between joint return distribution and its Bellman target. In experiments, our method accurately models the joint return distribution in environments with richly correlated reward functions, and outperforms previous RL methods utilizing multi-dimensional reward functions in the control setting.

RSL-RL is an open-source Reinforcement Learning library tailored to the specific needs of the robotics community. Unlike broad general-purpose frameworks, its design philosophy prioritizes a compact and easily modifiable codebase, allowing researchers to adapt and extend algorithms with minimal overhead. The library focuses on algorithms most widely adopted in robotics, together with auxiliary techniques that address robotics-specific challenges. Optimized for GPU-only training, RSL-RL achieves high-throughput performance in large-scale simulation environments. Its effectiveness has been validated in both simulation benchmarks and in real-world robotic experiments, demonstrating its utility as a lightweight, extensible, and practical framework to develop learning-based robotic controllers. The library is open-sourced at: https://github.com/leggedrobotics/rsl_rl.

The development of reasoning capabilities represents a critical frontier in large language models (LLMs) research, where reinforcement learning (RL) and process reward models (PRMs) have emerged as predominant methodological frameworks. Contrary to conventional wisdom, empirical evidence from DeepSeek-R1 demonstrates that pure RL training focused on mathematical problem-solving can progressively enhance reasoning abilities without PRM integration, challenging the perceived necessity of process supervision. In this study, we conduct a systematic investigation of the relationship between RL training and PRM capabilities. Our findings demonstrate that problem-solving proficiency and process supervision capabilities represent complementary dimensions of reasoning that co-evolve synergistically during pure RL training. In particular, current PRMs underperform simple baselines like majority voting when applied to state-of-the-art models such as DeepSeek-R1 and QwQ-32B. To address this limitation, we propose Self-PRM, an introspective framework in which models autonomously evaluate and rerank their generated solutions through self-reward mechanisms. Although Self-PRM consistently improves the accuracy of the benchmark (particularly with larger sample sizes), analysis exposes persistent challenges: The approach exhibits low precision (<10\%) on difficult problems, frequently misclassifying flawed solutions as valid. These analyses underscore the need for continued RL scaling to improve reward alignment and introspective accuracy. Overall, our findings suggest that PRM may not be essential for enhancing complex reasoning, as pure RL not only improves problem-solving skills but also inherently fosters robust PRM capabilities. We hope these findings provide actionable insights for building more reliable and self-aware complex reasoning models.

Reinforcement learning (RL) has been widely used in training large language models~(LLMs) for preventing unexpected outputs, \eg reducing harmfulness and errors. However, existing RL methods mostly adopt the instance-level reward, which is unable to provide fine-grained supervision for complex reasoning tasks, and can not focus on the few key tokens that lead to the incorrectness. To address it, we propose a new RL method named RLMEC that incorporates a generative model as the reward model, which is trained by the erroneous solution rewriting task under the minimum editing constraint, and can produce token-level rewards for RL training. Based on the generative reward model, we design the token-level RL objective for training and an imitation-based regularization for stabilizing RL process. And the both objectives focus on the learning of the key tokens for the erroneous solution, reducing the effect of other unimportant tokens. The experiment results on mathematical tasks and question-answering tasks have demonstrated the effectiveness of our approach. Our code and data are available at https://github.com/RUCAIBox/RLMEC.

Specifying rewards for reinforcement learned (RL) agents is challenging. Preference-based RL (PbRL) mitigates these challenges by inferring a reward from feedback over sets of trajectories. However, the effectiveness of PbRL is limited by the amount of feedback needed to reliably recover the structure of the target reward. We present the PRIor Over Rewards (PRIOR) framework, which incorporates priors about the structure of the reward function and the preference feedback into the reward learning process. Imposing these priors as soft constraints on the reward learning objective reduces the amount of feedback required by half and improves overall reward recovery. Additionally, we demonstrate that using an abstract state space for the computation of the priors further improves the reward learning and the agent's performance.

Reinforcement Learning with Verifiable Reward (RLVR) has significantly advanced the complex reasoning abilities of Large Language Models (LLMs). However, it struggles to break through the inherent capability boundaries of the base LLM, due to its essentially on-policy strategy coupled with LLM's immense action space and sparse reward. Critically, RLVR can lead to the capability boundary collapse, narrowing the LLM's problem-solving scope. To address this problem, we propose RL-PLUS, a novel hybrid-policy optimization approach for LLMs that synergizes internal exploitation with external data to achieve stronger reasoning capabilities and surpass the boundaries of base models. RL-PLUS integrates two core components, i.e., Multiple Importance Sampling to address distributional mismatch from external data, and Exploration-Based Advantage Function to guide the model towards high-value, unexplored reasoning paths. We provide both theoretical analysis and extensive experiments to demonstrate the superiority and generalizability of our approach. Compared with existing RLVR methods, RL-PLUS achieves 1) state-of-the-art performance on six math reasoning benchmarks; 2) superior performance on six out-of-distribution reasoning tasks; 3) consistent and significant gains across diverse model families, with average relative improvements up to 69.2\%. Moreover, the analysis of Pass@k curves indicates that RL-PLUS effectively resolves the capability boundary collapse problem.

Recent advances in Reinforcement Learning with Verifiable Rewards (RLVR) have empowered large language models (LLMs) to tackle challenging reasoning tasks such as mathematics and programming. RLVR leverages verifiable outcome rewards to guide policy optimization, enabling LLMs to progressively improve output quality in a grounded and reliable manner. Despite its promise, the RLVR paradigm poses significant challenges, as existing methods often suffer from sparse reward signals and unstable policy gradient updates, particularly in RL-based approaches. To address the challenges, we propose PACS, a novel RLVR framework that achieves imPlicit Actor Critic coupling via a Supervised learning framework. By treating the outcome reward as a predictable label, we reformulate the RLVR problem into a supervised learning task over a score function parameterized by the policy model and optimized using cross-entropy loss. A detailed gradient analysis shows that this supervised formulation inherently recovers the classical policy gradient update while implicitly coupling actor and critic roles, yielding more stable and efficient training. Benchmarking on challenging mathematical reasoning tasks, PACS outperforms strong RLVR baselines, such as PPO and GRPO, achieving superior reasoning performance. For instance, PACS achieves 59.78\% at pass@256 on AIME 2025, representing improvements of 13.32 and 14.36 points over PPO and GRPO. This simple yet powerful framework offers a promising avenue for LLMs post-training with verifiable rewards. Our code and data are available as open source at https://github.com/ritzz-ai/PACS.

Preference-based reinforcement learning (PbRL) is an approach that enables RL agents to learn from preference, which is particularly useful when formulating a reward function is challenging. Existing PbRL methods generally involve a two-step procedure: they first learn a reward model based on given preference data and then employ off-the-shelf reinforcement learning algorithms using the learned reward model. However, obtaining an accurate reward model solely from preference information, especially when the preference is from human teachers, can be difficult. Instead, we propose a PbRL algorithm that directly learns from preference without requiring any reward modeling. To achieve this, we adopt a contrastive learning framework to design a novel policy scoring metric that assigns a high score to policies that align with the given preferences. We apply our algorithm to offline RL tasks with actual human preference labels and show that our algorithm outperforms or is on par with the existing PbRL methods. Notably, on high-dimensional control tasks, our algorithm surpasses offline RL methods that learn with ground-truth reward information. Finally, we show that our algorithm can be successfully applied to fine-tune large language models.

Reinforcement Learning with Verifiable Rewards (RLVR) strengthens LLM reasoning, but training often oscillates between {entropy collapse} and {entropy explosion}. We trace both hazards to the mean baseline used in value-free RL (e.g., GRPO and DAPO), which improperly penalizes negative-advantage samples under reward outliers. We propose {Quantile Advantage Estimation} (QAE), replacing the mean with a group-wise K-quantile baseline. QAE induces a response-level, two-regime gate: on hard queries (p <= 1 - K) it reinforces rare successes, while on easy queries (p > 1 - K) it targets remaining failures. Under first-order softmax updates, we prove {two-sided entropy safety}, giving lower and upper bounds on one-step entropy change that curb explosion and prevent collapse. Empirically, this minimal modification stabilizes entropy, sparsifies credit assignment (with tuned K, roughly 80% of responses receive zero advantage), and yields sustained pass@1 gains on Qwen3-8B/14B-Base across AIME 2024/2025 and AMC 2023. These results identify {baseline design} -- rather than token-level heuristics -- as the primary mechanism for scaling RLVR.

Reinforcement learning (RL) holds significant promise for training LLM agents to handle complex, goal-oriented tasks that require multi-step interactions with external environments. However, a critical challenge when applying RL to these agentic tasks arises from delayed rewards: feedback signals are typically available only after the entire task is completed. This makes it non-trivial to assign delayed rewards to earlier actions, providing insufficient guidance regarding environmental constraints and hindering agent training. In this work, we draw on the insight that the ultimate completion of a task emerges from the cumulative progress an agent makes across individual steps. We propose Stepwise Progress Attribution (SPA), a general reward redistribution framework that decomposes the final reward into stepwise contributions, each reflecting its incremental progress toward overall task completion. To achieve this, we train a progress estimator that accumulates stepwise contributions over a trajectory to match the task completion. During policy optimization, we combine the estimated per-step contribution with a grounding signal for actions executed in the environment as the fine-grained, intermediate reward for effective agent training. Extensive experiments on common agent benchmarks (including Webshop, ALFWorld, and VirtualHome) demonstrate that SPA consistently outperforms the state-of-the-art method in both success rate (+2.5\% on average) and grounding accuracy (+1.9\% on average). Further analyses demonstrate that our method remarkably provides more effective intermediate rewards for RL training. Our code is available at https://github.com/WangHanLinHenry/SPA-RL-Agent.

Safe Reinforcement Learning (Safe RL) aims to ensure safety when an RL agent conducts learning by interacting with real-world environments where improper actions can induce high costs or lead to severe consequences. In this paper, we propose a novel Safe Skill Planning (SSkP) approach to enhance effective safe RL by exploiting auxiliary offline demonstration data. SSkP involves a two-stage process. First, we employ PU learning to learn a skill risk predictor from the offline demonstration data. Then, based on the learned skill risk predictor, we develop a novel risk planning process to enhance online safe RL and learn a risk-averse safe policy efficiently through interactions with the online RL environment, while simultaneously adapting the skill risk predictor to the environment. We conduct experiments in several benchmark robotic simulation environments. The experimental results demonstrate that the proposed approach consistently outperforms previous state-of-the-art safe RL methods.

Reinforcement Learning from Human Feedback (RLHF) has emerged as a dominant approach for aligning LLM outputs with human preferences. Inspired by the success of RLHF, we study the performance of multiple algorithms that learn from feedback (Expert Iteration, Proximal Policy Optimization (PPO), Return-Conditioned RL) on improving LLM reasoning capabilities. We investigate both sparse and dense rewards provided to the LLM both heuristically and via a learned reward model. We additionally start from multiple model sizes and initializations both with and without supervised fine-tuning (SFT) data. Overall, we find all algorithms perform comparably, with Expert Iteration performing best in most cases. Surprisingly, we find the sample complexity of Expert Iteration is similar to that of PPO, requiring at most on the order of 10^6 samples to converge from a pretrained checkpoint. We investigate why this is the case, concluding that during RL training models fail to explore significantly beyond solutions already produced by SFT models. Additionally, we discuss a trade off between maj@1 and pass@96 metric performance during SFT training and how conversely RL training improves both simultaneously. We then conclude by discussing the implications of our findings for RLHF and the future role of RL in LLM fine-tuning.

The goal of reinforcement learning (RL) is to find a policy that maximizes the expected cumulative return. It has been shown that this objective can be represented as an optimization problem of state-action visitation distribution under linear constraints. The dual problem of this formulation, which we refer to as dual RL, is unconstrained and easier to optimize. In this work, we first cast several state-of-the-art offline RL and offline imitation learning (IL) algorithms as instances of dual RL approaches with shared structures. Such unification allows us to identify the root cause of the shortcomings of prior methods. For offline IL, our analysis shows that prior methods are based on a restrictive coverage assumption that greatly limits their performance in practice. To fix this limitation, we propose a new discriminator-free method ReCOIL that learns to imitate from arbitrary off-policy data to obtain near-expert performance. For offline RL, our analysis frames a recent offline RL method XQL in the dual framework, and we further propose a new method f-DVL that provides alternative choices to the Gumbel regression loss that fixes the known training instability issue of XQL. The performance improvements by both of our proposed methods, ReCOIL and f-DVL, in IL and RL are validated on an extensive suite of simulated robot locomotion and manipulation tasks. Project code and details can be found at this https://hari-sikchi.github.io/dual-rl.

Applying Reinforcement Learning (RL) to sequence generation models enables the direct optimization of long-term rewards (e.g., BLEU and human feedback), but typically requires large-scale sampling over a space of action sequences. This is a computational challenge as presented by the practice of sequence generation problems, such as machine translation, where we often deal with a large action space (e.g., a vocabulary) and a long action sequence (e.g., a translation). In this work, we introduce two-stage sampling and dynamic sampling approaches to improve the sampling efficiency during training sequence generation models via RL. We experiment with our approaches on the traditional sequence generation tasks, including machine translation and abstractive summarization. Furthermore, we evaluate our approaches in RL from human feedback (RLHF) through training a large language model using the reward model. Experimental results show that the efficient sampling-based RL, referred to as ESRL, can outperform all baselines in terms of both training efficiency and memory consumption. Notably, ESRL yields consistent performance gains over the strong REINFORCE, minimum risk training, and proximal policy optimization methods.

This paper proposes a novel reinforcement learning (RL) framework for credit underwriting that tackles ungeneralizable contextual challenges. We adapt RL principles for credit scoring, incorporating action space renewal and multi-choice actions. Our work demonstrates that the traditional underwriting approach aligns with the RL greedy strategy. We introduce two new RL-based credit underwriting algorithms to enable more informed decision-making. Simulations show these new approaches outperform the traditional method in scenarios where the data aligns with the model. However, complex situations highlight model limitations, emphasizing the importance of powerful machine learning models for optimal performance. Future research directions include exploring more sophisticated models alongside efficient exploration mechanisms.

Reinforcement Learning and recently Deep Reinforcement Learning are popular methods for solving sequential decision making problems modeled as Markov Decision Processes. RL modeling of a problem and selecting algorithms and hyper-parameters require careful considerations as different configurations may entail completely different performances. These considerations are mainly the task of RL experts; however, RL is progressively becoming popular in other fields where the researchers and system designers are not RL experts. Besides, many modeling decisions, such as defining state and action space, size of batches and frequency of batch updating, and number of timesteps are typically made manually. For these reasons, automating different components of RL framework is of great importance and it has attracted much attention in recent years. Automated RL provides a framework in which different components of RL including MDP modeling, algorithm selection and hyper-parameter optimization are modeled and defined automatically. In this article, we explore the literature and present recent work that can be used in automated RL. Moreover, we discuss the challenges, open questions and research directions in AutoRL.

Recent work has shown that asking language models to generate reasoning steps improves performance on many reasoning tasks. When moving beyond prompting, this raises the question of how we should supervise such models: outcome-based approaches which supervise the final result, or process-based approaches which supervise the reasoning process itself? Differences between these approaches might naturally be expected not just in final-answer errors but also in reasoning errors, which can be difficult to detect and are problematic in many real-world domains such as education. We run the first comprehensive comparison between process- and outcome-based approaches trained on a natural language task, GSM8K. We find that pure outcome-based supervision produces similar final-answer error rates with less label supervision. However, for correct reasoning steps we find it necessary to use process-based supervision or supervision from learned reward models that emulate process-based feedback. In total, we improve the previous best results from 16.8% to 12.7% final-answer error and 14.0% to 3.4% reasoning error among final-answer-correct solutions.

Large reasoning models (LRMs) already possess a latent capacity for long chain-of-thought reasoning. Prior work has shown that outcome-based reinforcement learning (RL) can incidentally elicit advanced reasoning behaviors such as self-correction, backtracking, and verification phenomena often referred to as the model's "aha moment". However, the timing and consistency of these emergent behaviors remain unpredictable and uncontrollable, limiting the scalability and reliability of LRMs' reasoning capabilities. To address these limitations, we move beyond reliance on prompts and coincidental "aha moments". Instead, we explicitly align models with three meta-abilities: deduction, induction, and abduction, using automatically generated, self-verifiable tasks. Our three stage-pipeline individual alignment, parameter-space merging, and domain-specific reinforcement learning, boosting performance by over 10\% relative to instruction-tuned baselines. Furthermore, domain-specific RL from the aligned checkpoint yields an additional 2\% average gain in the performance ceiling across math, coding, and science benchmarks, demonstrating that explicit meta-ability alignment offers a scalable and dependable foundation for reasoning. Code is available at: https://github.com/zhiyuanhubj/Meta-Ability-Alignment

Sequential decision making, commonly formalized as Markov Decision Process (MDP) optimization, is a important challenge in artificial intelligence. Two key approaches to this problem are reinforcement learning (RL) and planning. This paper presents a survey of the integration of both fields, better known as model-based reinforcement learning. Model-based RL has two main steps. First, we systematically cover approaches to dynamics model learning, including challenges like dealing with stochasticity, uncertainty, partial observability, and temporal abstraction. Second, we present a systematic categorization of planning-learning integration, including aspects like: where to start planning, what budgets to allocate to planning and real data collection, how to plan, and how to integrate planning in the learning and acting loop. After these two sections, we also discuss implicit model-based RL as an end-to-end alternative for model learning and planning, and we cover the potential benefits of model-based RL. Along the way, the survey also draws connections to several related RL fields, like hierarchical RL and transfer learning. Altogether, the survey presents a broad conceptual overview of the combination of planning and learning for MDP optimization.

Multimodal Reward Models (MRMs) play a crucial role in enhancing the performance of Multimodal Large Language Models (MLLMs). While recent advancements have primarily focused on improving the model structure and training data of MRMs, there has been limited exploration into the effectiveness of long-term reasoning capabilities for reward modeling and how to activate these capabilities in MRMs. In this paper, we explore how Reinforcement Learning (RL) can be used to improve reward modeling. Specifically, we reformulate the reward modeling problem as a rule-based RL task. However, we observe that directly applying existing RL algorithms, such as Reinforce++, to reward modeling often leads to training instability or even collapse due to the inherent limitations of these algorithms. To address this issue, we propose the StableReinforce algorithm, which refines the training loss, advantage estimation strategy, and reward design of existing RL methods. These refinements result in more stable training dynamics and superior performance. To facilitate MRM training, we collect 200K preference data from diverse datasets. Our reward model, R1-Reward, trained using the StableReinforce algorithm on this dataset, significantly improves performance on multimodal reward modeling benchmarks. Compared to previous SOTA models, R1-Reward achieves a 8.4% improvement on the VL Reward-Bench and a 14.3% improvement on the Multimodal Reward Bench. Moreover, with more inference compute, R1-Reward's performance is further enhanced, highlighting the potential of RL algorithms in optimizing MRMs.

Reinforcement learning (RL) has become a standard paradigm for refining large language models (LLMs) beyond pre-training and instruction tuning. A prominent line of work is RL with verifiable rewards (RLVR), which leverages automatically verifiable outcomes (e.g., correctness or executability) to generate reward signals. While efficient, this framework faces two key limitations: First, its binary feedback is too sparse to capture the quality of the reasoning process. Second, its coarse-grained rewards potentially lead to vanishing gradients. Inspired by observations from human learning, we introduce a RL technique that integrates verifiable outcomes with the model's own confidence estimates. This joint design enriches the reward signal, providing finer-grained feedback and implicitly supervising the reasoning process. Experimental results demonstrate that our proposed method enhances RL performance across multiple datasets and reduces token consumption during inference, while incurring negligible additional training cost. Moreover, it can be used as a plug-in module to enhance other state-of-the-art RL methods.

Reinforcement learning with verifiable rewards (RLVR) improves language model reasoning by using rule-based rewards in verifiable domains such as mathematics and code. However, RLVR leads to limited generalization for open-ended tasks -- such as writing outline essays or making meal plans -- where humans reason routinely. This paper shows that the RLVR paradigm is effective beyond verifiable domains, and introduces **RL** with **M**odel-rewarded **T**hinking (**RLMT**) for general-purpose chat capabilities. Using diverse real-world prompts, RLMT requires LMs to generate long CoT reasoning before response, and optimizes them with online RL against a preference-based reward model used in RLHF. Across 40 training runs on Llama-3.1-8B and Qwen-2.5-7B (both base and instruct) and multiple optimization algorithms (DPO, PPO, and GRPO), RLMT consistently outperforms standard RLHF pipelines. This includes substantial gains of 3-7 points on three chat benchmarks (AlpacaEval2, WildBench, and ArenaHardV2), along with 1-3 point improvements on other tasks like creative writing and general knowledge. Our best 8B model surpasses GPT-4o in chat and creative writing and rivals Claude-3.7-Sonnet (Thinking). RLMT can also be applied directly to base models without an SFT stage, akin to R1-Zero training. Remarkably, with only 7K prompts, Llama-3.1-8B base trained with our RLMT recipe outperforms Llama-3.1-8B-Instruct post-trained with a complex multi-staged pipeline with 25M+ examples. We close with qualitative and quantitative analyses of how trained models plan their responses. Our results rethink the post-training pipeline and call upon future work to understand and employ thinking more broadly.

In recent years, Reinforcement Learning (RL) has been applied to real-world problems with increasing success. Such applications often require to put constraints on the agent's behavior. Existing algorithms for constrained RL (CRL) rely on gradient descent-ascent, but this approach comes with a caveat. While these algorithms are guaranteed to converge on average, they do not guarantee last-iterate convergence, i.e., the current policy of the agent may never converge to the optimal solution. In practice, it is often observed that the policy alternates between satisfying the constraints and maximizing the reward, rarely accomplishing both objectives simultaneously. Here, we address this problem by introducing Reinforcement Learning with Optimistic Ascent-Descent (ReLOAD), a principled CRL method with guaranteed last-iterate convergence. We demonstrate its empirical effectiveness on a wide variety of CRL problems including discrete MDPs and continuous control. In the process we establish a benchmark of challenging CRL problems.

Abstract Language Models (LMs) achieve substantial language capabilities when finetuned using Reinforcement Learning with Human Feedback (RLHF). However, RLHF is an unstable and data-hungry process that continually requires new high-quality LM-generated data for finetuning. We introduce Advantage-Leftover Lunch RL (A-LoL), a new class of offline policy gradient algorithms that enable RL training on any pre-existing data. By assuming the entire LM output sequence as a single action, A-LoL allows incorporating sequence-level classifiers or human-designed scoring functions as rewards. Subsequently, by using LM's internal sequence-level value estimate, A-LoL filters negative advantage (low-quality) data points during training, making it resilient to noise. Overall, A-LoL is an easy-to-implement LM training recipe that is sample-efficient and stable. We demonstrate the effectiveness of A-LoL and its variants with a set of four different language generation tasks. We compare against both online RL (PPO) and recent preference-based (DPO, PRO) and reward-based (GOLD) offline RL baselines. On the commonly-used RLHF benchmark, Helpful and Harmless Assistant (HHA), LMs trained with A-LoL methods achieve the highest diversity while also being rated more safe and helpful than baselines according to humans. Additionally, in the remaining three tasks, A-LoL could optimize multiple distinct reward functions even when using noisy or suboptimal training data. We also release our experimental code. https://github.com/abaheti95/LoL-RL

Reinforcement learning has been applied in operation research and has shown promise in solving large combinatorial optimization problems. However, existing works focus on developing neural network architectures for certain problems. These works lack the flexibility to incorporate recent advances in reinforcement learning, as well as the flexibility of customizing model architectures for operation research problems. In this work, we analyze the end-to-end autoregressive models for vehicle routing problems and show that these models can benefit from the recent advances in reinforcement learning with a careful re-implementation of the model architecture. In particular, we re-implemented the Attention Model and trained it with Proximal Policy Optimization (PPO) in CleanRL, showing at least 8 times speed up in training time. We hereby introduce RLOR, a flexible framework for Deep Reinforcement Learning for Operation Research. We believe that a flexible framework is key to developing deep reinforcement learning models for operation research problems. The code of our work is publicly available at https://github.com/cpwan/RLOR.

Reinforcement learning with verifiable outcome rewards (RLVR) has effectively scaled up chain-of-thought (CoT) reasoning in large language models (LLMs). Yet, its efficacy in training vision-language model (VLM) agents for goal-directed action reasoning in visual environments is less established. This work investigates this problem through extensive experiments on complex card games, such as 24 points, and embodied tasks from ALFWorld. We find that when rewards are based solely on action outcomes, RL fails to incentivize CoT reasoning in VLMs, instead leading to a phenomenon we termed thought collapse, characterized by a rapid loss of diversity in the agent's thoughts, state-irrelevant and incomplete reasoning, and subsequent invalid actions, resulting in negative rewards. To counteract thought collapse, we highlight the necessity of process guidance and propose an automated corrector that evaluates and refines the agent's reasoning at each RL step. This simple and scalable GTR (Guided Thought Reinforcement) framework trains reasoning and action simultaneously without the need for dense, per-step human labeling. Our experiments demonstrate that GTR significantly enhances the performance and generalization of the LLaVA-7b model across various visual environments, achieving 3-5 times higher task success rates compared to SoTA models with notably smaller model sizes.

Large Language Model (LLM) based listwise ranking has shown superior performance in many passage ranking tasks. With the development of Large Reasoning Models, many studies have demonstrated that step-by-step reasoning during test-time helps improve listwise ranking performance. However, due to the scarcity of reasoning-intensive training data, existing rerankers perform poorly in many complex ranking scenarios and the ranking ability of reasoning-intensive rerankers remains largely underdeveloped. In this paper, we first propose an automated reasoning-intensive training data synthesis framework, which sources training queries and passages from diverse domains and applies DeepSeek-R1 to generate high-quality training labels. A self-consistency data filtering mechanism is designed to ensure the data quality. To empower the listwise reranker with strong reasoning ability, we further propose a two-stage post-training approach, which includes a cold-start supervised fine-tuning (SFT) stage for reasoning pattern learning and a reinforcement learning (RL) stage for further ranking ability enhancement. During the RL stage, based on the nature of listwise ranking, we design a multi-view ranking reward, which is more effective than a ranking metric-based reward. Extensive experiments demonstrate that our trained reasoning-intensive reranker ReasonRank outperforms existing baselines significantly and also achieves much lower latency than pointwise reranker Rank1. Through further experiments, our ReasonRank has achieved state-of-the-art (SOTA) performance 40.6 on the BRIGHT leaderboard\footnote{https://brightbenchmark.github.io/.} Our codes are available at https://github.com/8421BCD/ReasonRank.

Reinforcement Learning from Human Feedback (RLHF) has emerged as a important paradigm for aligning large language models (LLMs) with human preferences during post-training. This framework typically involves two stages: first, training a reward model on human preference data, followed by optimizing the language model using reinforcement learning algorithms. However, current RLHF approaches may constrained by two limitations. First, existing RLHF frameworks often rely on Bradley-Terry models to assign scalar rewards based on pairwise comparisons of individual responses. However, this approach imposes significant challenges on reward model (RM), as the inherent variability in prompt-response pairs across different contexts demands robust calibration capabilities from the RM. Second, reward models are typically initialized from generative foundation models, such as pre-trained or supervised fine-tuned models, despite the fact that reward models perform discriminative tasks, creating a mismatch. This paper introduces Pairwise-RL, a RLHF framework that addresses these challenges through a combination of generative reward modeling and a pairwise proximal policy optimization (PPO) algorithm. Pairwise-RL unifies reward model training and its application during reinforcement learning within a consistent pairwise paradigm, leveraging generative modeling techniques to enhance reward model performance and score calibration. Experimental evaluations demonstrate that Pairwise-RL outperforms traditional RLHF frameworks across both internal evaluation datasets and standard public benchmarks, underscoring its effectiveness in improving alignment and model behavior.

Reinforcement learning (RL) is typically concerned with estimating stationary policies or single-step models, leveraging the Markov property to factorize problems in time. However, we can also view RL as a generic sequence modeling problem, with the goal being to produce a sequence of actions that leads to a sequence of high rewards. Viewed in this way, it is tempting to consider whether high-capacity sequence prediction models that work well in other domains, such as natural-language processing, can also provide effective solutions to the RL problem. To this end, we explore how RL can be tackled with the tools of sequence modeling, using a Transformer architecture to model distributions over trajectories and repurposing beam search as a planning algorithm. Framing RL as sequence modeling problem simplifies a range of design decisions, allowing us to dispense with many of the components common in offline RL algorithms. We demonstrate the flexibility of this approach across long-horizon dynamics prediction, imitation learning, goal-conditioned RL, and offline RL. Further, we show that this approach can be combined with existing model-free algorithms to yield a state-of-the-art planner in sparse-reward, long-horizon tasks.

Great successes have been reported using Reinforcement Learning from Human Feedback (RLHF) to align large language models. Open-source preference datasets and reward models have enabled wider experimentation beyond generic chat settings, particularly to make systems more "helpful" for tasks like web question answering, summarization, and multi-turn dialogue. When optimizing for helpfulness, RLHF has been consistently observed to drive models to produce longer outputs. This paper demonstrates that optimizing for response length is a significant factor behind RLHF's reported improvements in these settings. First, we study the relationship between reward and length for reward models trained on three open-source preference datasets for helpfulness. Here, length correlates strongly with reward, and improvements in reward score are driven in large part by shifting the distribution over output lengths. We then explore interventions during both RL and reward model learning to see if we can achieve the same downstream improvements as RLHF without increasing length. While our interventions mitigate length increases, they aren't uniformly effective across settings. Furthermore, we find that even running RLHF with a reward based solely on length can reproduce most of the downstream improvements over the initial policy model, showing that reward models in these settings have a long way to go.

Despite significant advancements in large language models (LLMs), a major drawback of reasoning models is their enormous token usage, which increases computational cost, resource requirements, and response time. In this work, we revisit the core principles of reinforcement learning (RL) and, through mathematical analysis, demonstrate that the tendency to generate lengthy responses arises inherently from RL-based optimization during training. This finding questions the prevailing assumption that longer responses inherently improve reasoning accuracy. Instead, we uncover a natural correlation between conciseness and accuracy that has been largely overlooked. Moreover, we show that introducing a secondary phase of RL post-training, using a small set of problems and limited resources, can significantly reduce a model's chain of thought while maintaining or even enhancing accuracy. Finally, we validate our conclusions through extensive experimental results.

DeepSeek-R1 has shown that long chain-of-thought (CoT) reasoning can naturally emerge through a simple reinforcement learning (RL) framework with rule-based rewards, where the training may directly start from the base models-a paradigm referred to as zero RL training. Most recent efforts to reproduce zero RL training have primarily focused on the Qwen2.5 model series, which may not be representative as we find the base models already exhibit strong instruction-following and self-reflection abilities. In this work, we investigate zero RL training across 10 diverse base models, spanning different families and sizes including LLama3-8B, Mistral-7B/24B, DeepSeek-Math-7B, Qwen2.5-math-7B, and all Qwen2.5 models from 0.5B to 32B. Leveraging several key design strategies-such as adjusting format reward and controlling query difficulty-we achieve substantial improvements in both reasoning accuracy and response length across most settings. However, by carefully monitoring the training dynamics, we observe that different base models exhibit distinct patterns during training. For instance, the increased response length does not always correlate with the emergence of certain cognitive behaviors such as verification (i.e., the "aha moment"). Notably, we observe the "aha moment" for the first time in small models not from the Qwen family. We share the key designs that enable successful zero RL training, along with our findings and practices. To facilitate further research, we open-source the code, models, and analysis tools.

Graphical User Interface (GUI) agents have demonstrated remarkable progress in automating complex user interface interactions through reinforcement learning. However, current approaches face a fundamental dilemma: offline RL enables stable training on pre-collected trajectories, but struggles with multi-step task execution for lack of trajectory-level reward signals; online RL captures these signals through environment interaction, but suffers from sparse rewards and prohibitive deployment costs. To address it, we present Semi-online Reinforcement Learning, a novel paradigm that simulates online RL on offline trajectories. During each rollout process, we preserve the original model output within the multi-turn dialogue, where a Patch Module adaptively recovers the divergence between rollout and expert trajectories. To capture long-term training signals, Semi-online RL introduces discounted future returns into the reward computation and optimizes the policy with weighted step-level and episode-level advantages. We further introduce Semi-Online Performance (SOP), a metric that aligns better with true online performance, serving as a practical and effective proxy for real-world evaluation. Experiments show that ours Semi-online RL achieves SOTA performance among 7B models across four dynamic benchmarks, with significant gains over the base model (e.g., +12.0% on AndroidWorld, +23.8% on AITW), demonstrating significant progress in bridging the gap between offline training efficiency and online multi-turn reasoning. The code is available at https://github.com/X-PLUG/MobileAgent/tree/main/UI-S1.

In this work, we study the issue of reward hacking on the response length, a challenge emerging in Reinforcement Learning from Human Feedback (RLHF) on LLMs. A well-formatted, verbose but less helpful response from the LLMs can often deceive LLMs or even human evaluators to achieve high scores. The same issue also holds for some reward models in RL. To address the challenges in both training and evaluation, we establish a more reliable evaluation protocol for comparing different training configurations, which inspects the trade-off between LLM evaluation score and response length obtained by varying training hyperparameters. Based on this evaluation, we conduct large-scale studies, where the results shed insights into the efficacy of hyperparameters and tricks used in RL on mitigating length bias. We further propose to improve the reward model by jointly training two linear heads on shared feature representations to predict the rewards, one trained to correlate with length, and the other trained to decorrelate with length and therefore focus more on the actual content. We then discard the length head in RL to prevent reward hacking on length. Experiments demonstrate that our approach almost eliminates the reward correlation with length, and improves the obtained policy by a significant margin.

Recent advances in large language models (LLMs) have demonstrated that reinforcement learning with verifiable rewards (RLVR) can significantly enhance reasoning abilities by directly optimizing correctness, rather than relying solely on supervised imitation. This paradigm has been extended to multimodal LLMs for complex video and image understanding tasks. However, while outcome-driven RL improves answer accuracy, it can inadvertently decouple the reasoning chain from the final answer, leading to situations where models produce inconsistency between the reasoning trace and final answer. In our experiments on multiple-choice visual question-answering tasks, the standard GRPO method yields only 79.7\% consistency on MMVU between the reasoning steps and the chosen answers, indicating frequent mismatches between answers and reasoning. To this end, we propose Answer-Consistent Reinforcement Learning (ACRE) that modifies the GRPO algorithm with an auxiliary consistency check. After the model generates a chain of thought and an initial answer for a given question, we shuffle the answer options and prompt the model again with the same reasoning trace to predict a second answer. We design a consistency-verification reward that grants a high reward only if both the original and the post-shuffle answers agree and are correct; otherwise, a lower reward is assigned accordingly. This mechanism penalizes reasoning-answer misalignment and discourages the model from relying on spurious patterns, such as option ordering biases. We evaluate ACRE on challenging Video Reasoning benchmarks and multimodal math reasoning benchmarks, achieving an average 2.2\% and 1.5\% improvement for Video Reasoning and Math Reasoning tasks over the GRPO baseline.

As AI systems become more capable, we would like to enlist their help to supervise other AIs. We experiment with methods for training a harmless AI assistant through self-improvement, without any human labels identifying harmful outputs. The only human oversight is provided through a list of rules or principles, and so we refer to the method as 'Constitutional AI'. The process involves both a supervised learning and a reinforcement learning phase. In the supervised phase we sample from an initial model, then generate self-critiques and revisions, and then finetune the original model on revised responses. In the RL phase, we sample from the finetuned model, use a model to evaluate which of the two samples is better, and then train a preference model from this dataset of AI preferences. We then train with RL using the preference model as the reward signal, i.e. we use 'RL from AI Feedback' (RLAIF). As a result we are able to train a harmless but non-evasive AI assistant that engages with harmful queries by explaining its objections to them. Both the SL and RL methods can leverage chain-of-thought style reasoning to improve the human-judged performance and transparency of AI decision making. These methods make it possible to control AI behavior more precisely and with far fewer human labels.

Reinforcement learning from human feedback (RLHF) has emerged as a powerful technique to make large language models (LLMs) more capable in complex settings. RLHF proceeds as collecting human preference data, training a reward model on said data, and optimizing a base ML model with respect to said reward for extrinsic evaluation metrics (e.g. MMLU, GSM8k). RLHF relies on many assumptions about how the various pieces fit together, such as a reward model capturing human preferences and an RL optimizer extracting the right signal from a reward model. As the RLHF process involves many distinct design decisions, it is easy to assume that multiple processes are correlated and therefore numerically linked. This apparent correlation is often not true, where reward models are easily overoptimized or RL optimizers can reduce performance on tasks not modeled in the data. Notable manifestations of models trained with imperfect RLHF systems are those that are prone to refusing basic requests for safety reasons or appearing lazy in generations. As chat model evaluation becomes increasingly nuanced, the reliance on a perceived link between reward model training, RL scores, and downstream performance drives these issues, which we describe as an objective mismatch. In this paper, we illustrate the causes of this issue, reviewing relevant literature from model-based reinforcement learning, and argue for solutions. By solving objective mismatch in RLHF, the ML models of the future will be more precisely aligned to user instructions for both safety and helpfulness.

Many problems, such as online ad display, can be formulated as online bipartite matching. The crucial challenge lies in the nature of sequentially-revealed online item information, based on which we make irreversible matching decisions at each step. While numerous expert online algorithms have been proposed with bounded worst-case competitive ratios, they may not offer satisfactory performance in average cases. On the other hand, reinforcement learning (RL) has been applied to improve the average performance, but it lacks robustness and can perform arbitrarily poorly. In this paper, we propose a novel RL-based approach to edge-weighted online bipartite matching with robustness guarantees (LOMAR), achieving both good average-case and worst-case performance. The key novelty of LOMAR is a new online switching operation which, based on a judicious condition to hedge against future uncertainties, decides whether to follow the expert's decision or the RL decision for each online item. We prove that for any rhoin[0,1], LOMAR is rho-competitive against any given expert online algorithm. To improve the average performance, we train the RL policy by explicitly considering the online switching operation. Finally, we run empirical experiments to demonstrate the advantages of LOMAR compared to existing baselines. Our code is available at: https://github.com/Ren-Research/LOMAR

This paper surveys research in the rapidly growing field of enhancing large language models (LLMs) with reinforcement learning (RL), a technique that enables LLMs to improve their performance by receiving feedback in the form of rewards based on the quality of their outputs, allowing them to generate more accurate, coherent, and contextually appropriate responses. In this work, we make a systematic review of the most up-to-date state of knowledge on RL-enhanced LLMs, attempting to consolidate and analyze the rapidly growing research in this field, helping researchers understand the current challenges and advancements. Specifically, we (1) detail the basics of RL; (2) introduce popular RL-enhanced LLMs; (3) review researches on two widely-used reward model-based RL techniques: Reinforcement Learning from Human Feedback (RLHF) and Reinforcement Learning from AI Feedback (RLAIF); and (4) explore Direct Preference Optimization (DPO), a set of methods that bypass the reward model to directly use human preference data for aligning LLM outputs with human expectations. We will also point out current challenges and deficiencies of existing methods and suggest some avenues for further improvements. Project page of this work can be found at: https://github.com/ShuheWang1998/Reinforcement-Learning-Enhanced-LLMs-A-Survey.

Two common approaches to sequential decision-making are AI planning (AIP) and reinforcement learning (RL). Each has strengths and weaknesses. AIP is interpretable, easy to integrate with symbolic knowledge, and often efficient, but requires an up-front logical domain specification and is sensitive to noise; RL only requires specification of rewards and is robust to noise but is sample inefficient and not easily supplied with external knowledge. We propose an integrative approach that combines high-level planning with RL, retaining interpretability, transfer, and efficiency, while allowing for robust learning of the lower-level plan actions. Our approach defines options in hierarchical reinforcement learning (HRL) from AIP operators by establishing a correspondence between the state transition model of AI planning problem and the abstract state transition system of a Markov Decision Process (MDP). Options are learned by adding intrinsic rewards to encourage consistency between the MDP and AIP transition models. We demonstrate the benefit of our integrated approach by comparing the performance of RL and HRL algorithms in both MiniGrid and N-rooms environments, showing the advantage of our method over the existing ones.

Deep reinforcement learning (RL) algorithms are predominantly evaluated by comparing their relative performance on a large suite of tasks. Most published results on deep RL benchmarks compare point estimates of aggregate performance such as mean and median scores across tasks, ignoring the statistical uncertainty implied by the use of a finite number of training runs. Beginning with the Arcade Learning Environment (ALE), the shift towards computationally-demanding benchmarks has led to the practice of evaluating only a small number of runs per task, exacerbating the statistical uncertainty in point estimates. In this paper, we argue that reliable evaluation in the few run deep RL regime cannot ignore the uncertainty in results without running the risk of slowing down progress in the field. We illustrate this point using a case study on the Atari 100k benchmark, where we find substantial discrepancies between conclusions drawn from point estimates alone versus a more thorough statistical analysis. With the aim of increasing the field's confidence in reported results with a handful of runs, we advocate for reporting interval estimates of aggregate performance and propose performance profiles to account for the variability in results, as well as present more robust and efficient aggregate metrics, such as interquartile mean scores, to achieve small uncertainty in results. Using such statistical tools, we scrutinize performance evaluations of existing algorithms on other widely used RL benchmarks including the ALE, Procgen, and the DeepMind Control Suite, again revealing discrepancies in prior comparisons. Our findings call for a change in how we evaluate performance in deep RL, for which we present a more rigorous evaluation methodology, accompanied with an open-source library rliable, to prevent unreliable results from stagnating the field.

Policy-based reinforcement learning currently plays an important role in improving LLMs on mathematical reasoning tasks. However, existing rollout-based reinforcement learning methods (GRPO, DAPO, GSPO, etc.) fail to explicitly consider LLMs' learning ability for samples of different difficulty levels, which is contrary to the human cognitive process of mathematical reasoning tasks from easy to difficult. Intuitively, we find that the variance of the rollout group's reward in RLVR partly reflects the difficulty of the current sample for LLMs. Samples that are too easy or too difficult have a lower variance, while samples with moderate difficulty have a higher variance. Based on this, we propose VCRL, a curriculum reinforcement learning framework that dynamically controls the difficulty of training samples based on the variance of group rewards. Experiments on five mathematical benchmarks and two models reveal the advantages of VCRL over the current LLM RL baselines.

Recently, Offline Reinforcement Learning (RL) has achieved remarkable progress with the emergence of various algorithms and datasets. However, these methods usually focus on algorithmic advancements, ignoring that many low-level implementation choices considerably influence or even drive the final performance. As a result, it becomes hard to attribute the progress in Offline RL as these choices are not sufficiently discussed and aligned in the literature. In addition, papers focusing on a dataset (e.g., D4RL) often ignore algorithms proposed on another dataset (e.g., RL Unplugged), causing isolation among the algorithms, which might slow down the overall progress. Therefore, this work aims to bridge the gaps caused by low-level choices and datasets. To this end, we empirically investigate 20 implementation choices using three representative algorithms (i.e., CQL, CRR, and IQL) and present a guidebook for choosing implementations. Following the guidebook, we find two variants CRR+ and CQL+ , achieving new state-of-the-art on D4RL. Moreover, we benchmark eight popular offline RL algorithms across datasets under unified training and evaluation framework. The findings are inspiring: the success of a learning paradigm severely depends on the data distribution, and some previous conclusions are biased by the dataset used. Our code is available at https://github.com/sail-sg/offbench.

We consider the problem of preference based reinforcement learning (PbRL), where, unlike traditional reinforcement learning, an agent receives feedback only in terms of a 1 bit (0/1) preference over a trajectory pair instead of absolute rewards for them. The success of the traditional RL framework crucially relies on the underlying agent-reward model, which, however, depends on how accurately a system designer can express an appropriate reward function and often a non-trivial task. The main novelty of our framework is the ability to learn from preference-based trajectory feedback that eliminates the need to hand-craft numeric reward models. This paper sets up a formal framework for the PbRL problem with non-markovian rewards, where the trajectory preferences are encoded by a generalized linear model of dimension d. Assuming the transition model is known, we then propose an algorithm with almost optimal regret guarantee of mathcal{O}left( SH d log (T / delta) T right). We further, extend the above algorithm to the case of unknown transition dynamics, and provide an algorithm with near optimal regret guarantee mathcal{O}((d + H^2 + |S|)dT +|mathcal{S||A|TH} ). To the best of our knowledge, our work is one of the first to give tight regret guarantees for preference based RL problems with trajectory preferences.

While large language models show promise in medical applications, achieving expert-level clinical reasoning remains challenging due to the need for both accurate answers and transparent reasoning processes. To address this challenge, we introduce Fleming-R1, a model designed for verifiable medical reasoning through three complementary innovations. First, our Reasoning-Oriented Data Strategy (RODS) combines curated medical QA datasets with knowledge-graph-guided synthesis to improve coverage of underrepresented diseases, drugs, and multi-hop reasoning chains. Second, we employ Chain-of-Thought (CoT) cold start to distill high-quality reasoning trajectories from teacher models, establishing robust inference priors. Third, we implement a two-stage Reinforcement Learning from Verifiable Rewards (RLVR) framework using Group Relative Policy Optimization, which consolidates core reasoning skills while targeting persistent failure modes through adaptive hard-sample mining. Across diverse medical benchmarks, Fleming-R1 delivers substantial parameter-efficient improvements: the 7B variant surpasses much larger baselines, while the 32B model achieves near-parity with GPT-4o and consistently outperforms strong open-source alternatives. These results demonstrate that structured data design, reasoning-oriented initialization, and verifiable reinforcement learning can advance clinical reasoning beyond simple accuracy optimization. We release Fleming-R1 publicly to promote transparent, reproducible, and auditable progress in medical AI, enabling safer deployment in high-stakes clinical environments.

Large language models (LLMs) have demonstrated strong capabilities in language understanding and reasoning, yet they remain limited when tackling real-world tasks that require up-to-date knowledge, precise operations, or specialized tool use. To address this, we propose Tool-R1, a reinforcement learning framework that enables LLMs to perform general, compositional, and multi-step tool use by generating executable Python code. Tool-R1 supports integration of user-defined tools and standard libraries, with variable sharing across steps to construct coherent workflows. An outcome-based reward function, combining LLM-based answer judgment and code execution success, guides policy optimization. To improve training efficiency, we maintain a dynamic sample queue to cache and reuse high-quality trajectories, reducing the overhead of costly online sampling. Experiments on the GAIA benchmark show that Tool-R1 substantially improves both accuracy and robustness, achieving about 10\% gain over strong baselines, with larger improvements on complex multi-step tasks. These results highlight the potential of Tool-R1 for enabling reliable and efficient tool-augmented reasoning in real-world applications. Our code will be available at https://github.com/YBYBZhang/Tool-R1.

Reinforcement learning (RL) has become a powerful approach for improving the reasoning capabilities of large language models (LLMs), as evidenced by recent successes such as OpenAI's o1 and Deepseek-R1. However, applying RL at scale remains intimidatingly resource-intensive, requiring multiple model copies and extensive GPU workloads. On the other hand, while being powerful, recent studies suggest that RL does not fundamentally endow models with new knowledge; rather, it primarily reshapes the model's output distribution to activate reasoning capabilities latent in the base model. Building on this insight, we hypothesize that the changes in output probabilities induced by RL are largely model-size invariant, opening the door to a more efficient paradigm: training a small model with RL and transferring its induced probability shifts to larger base models. To verify our hypothesis, we conduct a token-level analysis of decoding trajectories and find high alignment in RL-induced output distributions across model scales, validating our hypothesis. Motivated by this, we propose RAST, a simple yet effective method that transfers reasoning behaviors by injecting RL-induced probability adjustments from a small RL-trained model into larger models. Experiments across multiple mathematical reasoning benchmarks show that RAST substantially and consistently enhances the reasoning capabilities of base models while requiring significantly lower GPU memory than direct RL training, sometimes even yielding better performance than the RL-trained counterparts. Our findings offer new insights into the nature of RL-driven reasoning and practical strategies for scaling its benefits without incurring its full computational cost. The project page of RAST is available at https://ozyyshr.github.io/RAST/.

Offline preference-based reinforcement learning (PbRL) typically operates in two phases: first, use human preferences to learn a reward model and annotate rewards for a reward-free offline dataset; second, learn a policy by optimizing the learned reward via offline RL. However, accurately modeling step-wise rewards from trajectory-level preference feedback presents inherent challenges. The reward bias introduced, particularly the overestimation of predicted rewards, leads to optimistic trajectory stitching, which undermines the pessimism mechanism critical to the offline RL phase. To address this challenge, we propose In-Dataset Trajectory Return Regularization (DTR) for offline PbRL, which leverages conditional sequence modeling to mitigate the risk of learning inaccurate trajectory stitching under reward bias. Specifically, DTR employs Decision Transformer and TD-Learning to strike a balance between maintaining fidelity to the behavior policy with high in-dataset trajectory returns and selecting optimal actions based on high reward labels. Additionally, we introduce an ensemble normalization technique that effectively integrates multiple reward models, balancing the tradeoff between reward differentiation and accuracy. Empirical evaluations on various benchmarks demonstrate the superiority of DTR over other state-of-the-art baselines.

Reinforcement learning (RL) with rule-based rewards has demonstrated strong potential in enhancing the reasoning and generalization capabilities of vision-language models (VLMs) and large language models (LLMs), while reducing computational overhead. However, its application in medical imaging remains underexplored. Existing reinforcement fine-tuning (RFT) approaches in this domain primarily target closed-ended visual question answering (VQA), limiting their applicability to real-world clinical reasoning. In contrast, open-ended medical VQA better reflects clinical practice but has received limited attention. While some efforts have sought to unify both formats via semantically guided RL, we observe that model-based semantic rewards often suffer from reward collapse, where responses with significant semantic differences receive similar scores. To address this, we propose ARMed (Adaptive Reinforcement for Medical Reasoning), a novel RL framework for open-ended medical VQA. ARMed first incorporates domain knowledge through supervised fine-tuning (SFT) on chain-of-thought data, then applies reinforcement learning with textual correctness and adaptive semantic rewards to enhance reasoning quality. We evaluate ARMed on six challenging medical VQA benchmarks. Results show that ARMed consistently boosts both accuracy and generalization, achieving a 32.64% improvement on in-domain tasks and an 11.65% gain on out-of-domain benchmarks. These results highlight the critical role of reward discriminability in medical RL and the promise of semantically guided rewards for enabling robust and clinically meaningful multimodal reasoning.

The success of many RL techniques heavily relies on human-engineered dense rewards, which typically demand substantial domain expertise and extensive trial and error. In our work, we propose DrS (Dense reward learning from Stages), a novel approach for learning reusable dense rewards for multi-stage tasks in a data-driven manner. By leveraging the stage structures of the task, DrS learns a high-quality dense reward from sparse rewards and demonstrations if given. The learned rewards can be reused in unseen tasks, thus reducing the human effort for reward engineering. Extensive experiments on three physical robot manipulation task families with 1000+ task variants demonstrate that our learned rewards can be reused in unseen tasks, resulting in improved performance and sample efficiency of RL algorithms. The learned rewards even achieve comparable performance to human-engineered rewards on some tasks. See our project page (https://sites.google.com/view/iclr24drs) for more details.

The functionality of Large Language Model (LLM) agents is primarily determined by two capabilities: action planning and answer summarization. The former, action planning, is the core capability that dictates an agent's performance. However, prevailing training paradigms employ end-to-end, multi-objective optimization that jointly trains both capabilities. This paradigm faces two critical challenges: imbalanced optimization objective allocation and scarcity of verifiable data, making it difficult to enhance the agent's planning capability. To address these challenges, we propose Reinforcement Learning with Tool-use Rewards (RLTR), a novel framework that decouples the training process to enable a focused, single-objective optimization of the planning module. Crucially, RLTR introduces a reward signal based on tool-use completeness to directly evaluate the quality of tool invocation sequences. This method offers a more direct and reliable training signal than assessing the final response content, thereby obviating the need for verifiable data. Our experiments demonstrate that RLTR achieves an 8%-12% improvement in planning performance compared to end-to-end baselines. Moreover, this enhanced planning capability, in turn, translates to a 5%-6% increase in the final response quality of the overall agent system.

Large language model (LLM) agents need to perform multi-turn interactions in real-world tasks. However, existing multi-turn RL algorithms for optimizing LLM agents fail to perform effective credit assignment over multiple turns while leveraging the generalization capabilities of LLMs and it remains unclear how to develop such algorithms. To study this, we first introduce a new benchmark, ColBench, where an LLM agent interacts with a human collaborator over multiple turns to solve realistic tasks in backend programming and frontend design. Building on this benchmark, we propose a novel RL algorithm, SWEET-RL (RL with Step-WisE Evaluation from Training-time information), that uses a carefully designed optimization objective to train a critic model with access to additional training-time information. The critic provides step-level rewards for improving the policy model. Our experiments demonstrate that SWEET-RL achieves a 6% absolute improvement in success and win rates on ColBench compared to other state-of-the-art multi-turn RL algorithms, enabling Llama-3.1-8B to match or exceed the performance of GPT4-o in realistic collaborative content creation.

Reinforcement learning (RL) tasks are typically framed as Markov Decision Processes (MDPs), assuming that decisions are made at fixed time intervals. However, many applications of great importance, including healthcare, do not satisfy this assumption, yet they are commonly modelled as MDPs after an artificial reshaping of the data. In addition, most healthcare (and similar) problems are offline by nature, allowing for only retrospective studies. To address both challenges, we begin by discussing the Semi-MDP (SMDP) framework, which formally handles actions of variable timings. We next present a formal way to apply SMDP modifications to nearly any given value-based offline RL method. We use this theory to introduce three SMDP-based offline RL algorithms, namely, SDQN, SDDQN, and SBCQ. We then experimentally demonstrate that only these SMDP-based algorithms learn the optimal policy in variable-time environments, whereas their MDP counterparts do not. Finally, we apply our new algorithms to a real-world offline dataset pertaining to warfarin dosing for stroke prevention and demonstrate similar results.

Training models to effectively use test-time compute is crucial for improving the reasoning performance of LLMs. Current methods mostly do so via fine-tuning on search traces or running RL with 0/1 outcome reward, but do these approaches efficiently utilize test-time compute? Would these approaches continue to scale as the budget improves? In this paper, we try to answer these questions. We formalize the problem of optimizing test-time compute as a meta-reinforcement learning (RL) problem, which provides a principled perspective on spending test-time compute. This perspective enables us to view the long output stream from the LLM as consisting of several episodes run at test time and leads us to use a notion of cumulative regret over output tokens as a way to measure the efficacy of test-time compute. Akin to how RL algorithms can best tradeoff exploration and exploitation over training, minimizing cumulative regret would also provide the best balance between exploration and exploitation in the token stream. While we show that state-of-the-art models do not minimize regret, one can do so by maximizing a dense reward bonus in conjunction with the outcome 0/1 reward RL. This bonus is the ''progress'' made by each subsequent block in the output stream, quantified by the change in the likelihood of eventual success. Using these insights, we develop Meta Reinforcement Fine-Tuning, or MRT, a new class of fine-tuning methods for optimizing test-time compute. MRT leads to a 2-3x relative gain in performance and roughly a 1.5x gain in token efficiency for math reasoning compared to outcome-reward RL.

Offline reinforcement learning algorithms hold the promise of enabling data-driven RL methods that do not require costly or dangerous real-world exploration and benefit from large pre-collected datasets. This in turn can facilitate real-world applications, as well as a more standardized approach to RL research. Furthermore, offline RL methods can provide effective initializations for online finetuning to overcome challenges with exploration. However, evaluating progress on offline RL algorithms requires effective and challenging benchmarks that capture properties of real-world tasks, provide a range of task difficulties, and cover a range of challenges both in terms of the parameters of the domain (e.g., length of the horizon, sparsity of rewards) and the parameters of the data (e.g., narrow demonstration data or broad exploratory data). While considerable progress in offline RL in recent years has been enabled by simpler benchmark tasks, the most widely used datasets are increasingly saturating in performance and may fail to reflect properties of realistic tasks. We propose a new benchmark for offline RL that focuses on realistic simulations of robotic manipulation and locomotion environments, based on models of real-world robotic systems, and comprising a variety of data sources, including scripted data, play-style data collected by human teleoperators, and other data sources. Our proposed benchmark covers state-based and image-based domains, and supports both offline RL and online fine-tuning evaluation, with some of the tasks specifically designed to require both pre-training and fine-tuning. We hope that our proposed benchmark will facilitate further progress on both offline RL and fine-tuning algorithms. Website with code, examples, tasks, and data is available at https://sites.google.com/view/d5rl/

The success of Deepseek-R1 has drawn the LLM community's attention to reinforcement learning (RL) methods like GRPO. However, such rule-based 0/1 outcome reward methods lack the capability to regulate the intermediate reasoning processes during chain-of-thought (CoT) generation, leading to severe overthinking phenomena. In response, recent studies have designed reward functions to reinforce models' behaviors in producing shorter yet correct completions. Nevertheless, we observe that these length-penalty reward functions exacerbate RL training instability: as the completion length decreases, model accuracy abruptly collapses, often occurring early in training. To address this issue, we propose a simple yet effective solution GRPO-lambda, an efficient and stabilized variant of GRPO, which dynamically adjusts the reward strategy by monitoring the correctness ratio among completions within each query-sampled group. A low correctness ratio indicates the need to avoid length penalty that compromises CoT quality, triggering a switch to length-agnostic 0/1 rewards that prioritize reasoning capability. A high ratio maintains length penalties to boost efficiency. Experimental results show that our approach avoids training instability caused by length penalty while maintaining the optimal accuracy-efficiency trade-off. On the GSM8K, GPQA, MATH-500, AMC 2023, and AIME 2024 benchmarks, it improves average accuracy by 1.48% while reducing CoT sequence length by 47.3%.

Reinforcement learning with verifiable rewards (RLVR) has achieved remarkable success in enhancing the reasoning capabilities of large language models (LLMs). However, existing RLVR methods often suffer from exploration inefficiency due to mismatches between the training data's difficulty and the model's capability. LLMs fail to discover viable reasoning paths when problems are overly difficult, while learning little new capability when problems are too simple. In this work, we formalize the impact of problem difficulty by quantifying the relationship between loss descent speed and rollout accuracy. Building on this analysis, we propose SEELE, a novel supervision-aided RLVR framework that dynamically adjusts problem difficulty to stay within the high-efficiency region. SEELE augments each training sample by appending a hint (part of a full solution) after the original problem. Unlike previous hint-based approaches, SEELE deliberately and adaptively adjusts the hint length for each problem to achieve an optimal difficulty. To determine the optimal hint length, SEELE employs a multi-round rollout sampling strategy. In each round, it fits an item response theory model to the accuracy-hint pairs collected in preceding rounds to predict the required hint length for the next round. This instance-level, real-time difficulty adjustment aligns problem difficulty with the evolving model capability, thereby improving exploration efficiency. Experimental results show that SEELE outperforms Group Relative Policy Optimization (GRPO) and Supervised Fine-tuning (SFT) by +11.8 and +10.5 points, respectively, and surpasses the best previous supervision-aided approach by +3.6 points on average across six math reasoning benchmarks.

Reinforcement learning (RL) for large language models is an energy-intensive endeavor: training can be unstable, and the policy may gradually drift away from its pretrained weights. We present RLEP\, -- \,Reinforcement Learning with Experience rePlay\, -- \,a two-phase framework that first collects verified trajectories and then replays them during subsequent training. At every update step, the policy is optimized on mini-batches that blend newly generated rollouts with these replayed successes. By replaying high-quality examples, RLEP steers the model away from fruitless exploration, focuses learning on promising reasoning paths, and delivers both faster convergence and stronger final performance. On the Qwen2.5-Math-7B base model, RLEP reaches baseline peak accuracy with substantially fewer updates and ultimately surpasses it, improving accuracy on AIME-2024 from 38.2% to 39.9%, on AIME-2025 from 19.8% to 22.3%, and on AMC-2023 from 77.0% to 82.2%. Our code, datasets, and checkpoints are publicly available at https://github.com/Kwai-Klear/RLEP to facilitate reproducibility and further research.

Current Large Language Models (LLMs) exhibit significant limitations, notably in structured, interpretable, and verifiable medical reasoning, alongside practical deployment challenges related to computational resources and data privacy. This report focused on the development of WiNGPT-3.0, the 32-billion parameter LLMs, engineered with the objective of enhancing its capacity for medical reasoning and exploring its potential for effective integration within healthcare IT infrastructures. The broader aim is to advance towards clinically applicable models. The approach involved a multi-stage training pipeline tailored for general, medical, and clinical reasoning. This pipeline incorporated supervised fine-tuning (SFT) and reinforcement learning (RL), leveraging curated Long Chain-of-Thought (CoT) datasets, auxiliary reward models, and an evidence-based diagnostic chain simulation. WiNGPT-3.0 demonstrated strong performance: specific model variants achieved scores of 66.6 on MedCalc and 87.1 on MedQA-USMLE. Furthermore, targeted training improved performance on a clinical reasoning task from a baseline score of 58.1 to 62.5. These findings suggest that reinforcement learning, even when applied with a limited dataset of only a few thousand examples, can enhance medical reasoning accuracy. Crucially, this demonstration of RL's efficacy with limited data and computation paves the way for more trustworthy and practically deployable LLMs within clinical workflows and health information infrastructures.

Reinforcement Learning from Verifiable Rewards (RLVR) has emerged as a powerful paradigm for enhancing Large Language Models (LLMs), exemplified by the success of OpenAI's o-series. In RLVR, rewards are derived from verifiable signals-such as passing unit tests in code generation or matching correct answers in mathematical reasoning. While effective, this requirement largely confines RLVR to domains with automatically checkable outcomes. To overcome this, we extend the RLVR paradigm to open-ended tasks by integrating rubric-based rewards, where carefully designed rubrics serve as structured, model-interpretable criteria for automatic scoring of subjective outputs. We construct, to our knowledge, the largest rubric reward system to date, with over 10,000 rubrics from humans, LLMs, or a hybrid human-LLM collaboration. Implementing rubric-based RL is challenging; we tackle these issues with a clear framework and present an open-sourced Qwen-30B-A3B model with notable gains: 1) With only 5K+ samples, our system improves by +5.2% on open-ended benchmarks (especially humanities), outperforming a 671B DeepSeek-V3 model by +2.4%, while preserving general and reasoning abilities. 2) Our method provides fine-grained stylistic control, using rubrics as anchors to mitigate the "AI-like" tone and produce more human-like, expressive responses. We share key lessons in rubric construction, data selection, and training, and discuss limitations and future releases.

Large language models (LLMs) have shown promise in performing complex multi-step reasoning, yet they continue to struggle with mathematical reasoning, often making systematic errors. A promising solution is reinforcement learning (RL) guided by reward models, particularly those focusing on process rewards, which score each intermediate step rather than solely evaluating the final outcome. This approach is more effective at guiding policy models towards correct reasoning trajectories. In this work, we propose an entropy-regularized process reward model (ER-PRM) that integrates KL-regularized Markov Decision Processes (MDP) to balance policy optimization with the need to prevent the policy from shifting too far from its initial distribution. We derive a novel reward construction method based on the theoretical results. Our theoretical analysis shows that we could derive the optimal reward model from the initial policy sampling. Our empirical experiments on the MATH and GSM8K benchmarks demonstrate that ER-PRM consistently outperforms existing process reward models, achieving 1% improvement on GSM8K and 2-3% improvement on MATH under best-of-N evaluation, and more than 1% improvement under RLHF. These results highlight the efficacy of entropy-regularization in enhancing LLMs' reasoning capabilities.

Reinforcement Learning with Human Feedback (RLHF) and Reinforcement Learning with Verifiable Rewards (RLVR) are the main RL paradigms used in LLM post-training, each offering distinct advantages. However, RLHF struggles with interpretability and reward hacking because it relies on human judgments that usually lack explicit criteria, whereas RLVR is limited in scope by its focus on correctness-based verifiers. We propose Reinforcement Learning with Binary Flexible Feedback (RLBFF), which combines the versatility of human-driven preferences with the precision of rule-based verification, enabling reward models to capture nuanced aspects of response quality beyond mere correctness. RLBFF extracts principles that can be answered in a binary fashion (e.g. accuracy of information: yes, or code readability: no) from natural language feedback. Such principles can then be used to ground Reward Model training as an entailment task (response satisfies or does not satisfy an arbitrary principle). We show that Reward Models trained in this manner can outperform Bradley-Terry models when matched for data and achieve top performance on RM-Bench (86.2%) and JudgeBench (81.4%, #1 on leaderboard as of September 24, 2025). Additionally, users can specify principles of interest at inference time to customize the focus of our reward models, in contrast to Bradley-Terry models. Finally, we present a fully open source recipe (including data) to align Qwen3-32B using RLBFF and our Reward Model, to match or exceed the performance of o3-mini and DeepSeek R1 on general alignment benchmarks of MT-Bench, WildBench, and Arena Hard v2 (at <5% of the inference cost).

We introduce CAMRL, the first curriculum-based asymmetric multi-task learning (AMTL) algorithm for dealing with multiple reinforcement learning (RL) tasks altogether. To mitigate the negative influence of customizing the one-off training order in curriculum-based AMTL, CAMRL switches its training mode between parallel single-task RL and asymmetric multi-task RL (MTRL), according to an indicator regarding the training time, the overall performance, and the performance gap among tasks. To leverage the multi-sourced prior knowledge flexibly and to reduce negative transfer in AMTL, we customize a composite loss with multiple differentiable ranking functions and optimize the loss through alternating optimization and the Frank-Wolfe algorithm. The uncertainty-based automatic adjustment of hyper-parameters is also applied to eliminate the need of laborious hyper-parameter analysis during optimization. By optimizing the composite loss, CAMRL predicts the next training task and continuously revisits the transfer matrix and network weights. We have conducted experiments on a wide range of benchmarks in multi-task RL, covering Gym-minigrid, Meta-world, Atari video games, vision-based PyBullet tasks, and RLBench, to show the improvements of CAMRL over the corresponding single-task RL algorithm and state-of-the-art MTRL algorithms. The code is available at: https://github.com/huanghanchi/CAMRL

Reinforcement learning (RL) promises a framework for near-universal problem-solving. In practice however, RL algorithms are often tailored to specific benchmarks, relying on carefully tuned hyperparameters and algorithmic choices. Recently, powerful model-based RL methods have shown impressive general results across benchmarks but come at the cost of increased complexity and slow run times, limiting their broader applicability. In this paper, we attempt to find a unifying model-free deep RL algorithm that can address a diverse class of domains and problem settings. To achieve this, we leverage model-based representations that approximately linearize the value function, taking advantage of the denser task objectives used by model-based RL while avoiding the costs associated with planning or simulated trajectories. We evaluate our algorithm, MR.Q, on a variety of common RL benchmarks with a single set of hyperparameters and show a competitive performance against domain-specific and general baselines, providing a concrete step towards building general-purpose model-free deep RL algorithms.

Recent advances have shown success in eliciting strong reasoning abilities in multimodal large language models (MLLMs) through rule-based reinforcement learning (RL) with outcome rewards. However, this paradigm typically lacks supervision over the thinking process leading to the final outcome.As a result, the model may learn sub-optimal reasoning strategies, which can hinder its generalization ability. In light of this, we propose SophiaVL-R1, as an attempt to add reward signals for the thinking process in this paradigm. To achieve this, we first train a thinking reward model that evaluates the quality of the entire thinking process. Given that the thinking reward may be unreliable for certain samples due to reward hacking, we propose the Trust-GRPO method, which assigns a trustworthiness weight to the thinking reward during training. This weight is computed based on the thinking reward comparison of responses leading to correct answers versus incorrect answers, helping to mitigate the impact of potentially unreliable thinking rewards. Moreover, we design an annealing training strategy that gradually reduces the thinking reward over time, allowing the model to rely more on the accurate rule-based outcome reward in later training stages. Experiments show that our SophiaVL-R1 surpasses a series of reasoning MLLMs on various benchmarks (e.g., MathVisita, MMMU), demonstrating strong reasoning and generalization capabilities. Notably, our SophiaVL-R1-7B even outperforms LLaVA-OneVision-72B on most benchmarks, despite the latter having 10 times more parameters. All code, models, and datasets are made publicly available at https://github.com/kxfan2002/SophiaVL-R1.

Reward sparsity in long-horizon reinforcement learning (RL) tasks remains a significant challenge, while existing outcome-based reward shaping struggles to define meaningful immediate rewards without introducing bias or requiring explicit task decomposition. Alternatively, verification-based reward shaping uses stepwise critics, but misalignment between immediate rewards and long-term objectives can lead to reward hacking and suboptimal policies. In this work, we address this problem in the context of software engineering (SWE) tasks, where multi-turn reasoning and rule-based verification are critical. We introduce the SWE-oriented RL Framework, a unified system supporting multi-turn interaction, docker-based execution, and customizable reward functions. Additionally, we propose Gated Reward Accumulation (G-RA), a novel method that accumulates immediate rewards only when high-level (long-term) rewards meet a predefined threshold, ensuring stable RL optimization. Experiments on SWE-bench Verified and kBench demonstrate that G-RA leads to an increase in completion rates (47.6\% \rightarrow 93.8\% and 22.0\% \rightarrow 86.0\%) and modification rates (19.6\% \rightarrow 23.8\% and 12.0\% \rightarrow 42.0\%), while avoiding policy degradation caused by reward misalignment. Our findings highlight the importance of balanced reward accumulation in long-horizon RL and provide a practical solution.

Preference-based Reinforcement Learning (PbRL) is a paradigm in which an RL agent learns to optimize a task using pair-wise preference-based feedback over trajectories, rather than explicit reward signals. While PbRL has demonstrated practical success in fine-tuning language models, existing theoretical work focuses on regret minimization and fails to capture most of the practical frameworks. In this study, we fill in such a gap between theoretical PbRL and practical algorithms by proposing a theoretical reward-agnostic PbRL framework where exploratory trajectories that enable accurate learning of hidden reward functions are acquired before collecting any human feedback. Theoretical analysis demonstrates that our algorithm requires less human feedback for learning the optimal policy under preference-based models with linear parameterization and unknown transitions, compared to the existing theoretical literature. Specifically, our framework can incorporate linear and low-rank MDPs with efficient sample complexity. Additionally, we investigate reward-agnostic RL with action-based comparison feedback and introduce an efficient querying algorithm tailored to this scenario.

Reinforcement Learning with Verifiable Rewards (RLVR) has recently demonstrated notable success in enhancing the reasoning capabilities of LLMs, particularly in mathematics and programming tasks. It is widely believed that RLVR enables LLMs to continuously self-improve, thus acquiring novel reasoning abilities that exceed corresponding base models' capacity. In this study, however, we critically re-examines this assumption by measuring the pass@k metric with large values of k to explore the reasoning capability boundary of the models across a wide range of model families and benchmarks. Surprisingly, the RL does not, in fact, elicit fundamentally new reasoning patterns. While RL-trained models outperform their base models at smaller values of k (\eg, k=1), base models can achieve a comparable or even higher pass@k score compared to their RL counterparts at large k values. The reasoning paths generated by RL-trained models are already included in the base models' sampling distribution, suggesting that most reasoning abilities manifested in RL-trained models are already obtained by base models. Further analysis shows that RL training boosts the performance by biasing the model's output distribution toward paths that are more likely to yield rewards, therefore sampling correct responses more efficiently. But this also results in a narrower reasoning capability boundary compared to base models. Similar results are observed in visual reasoning tasks trained with RLVR. Moreover, we find that distillation can genuinely introduce new knowledge into the model, different from RLVR. These findings underscore a critical limitation of RLVR in advancing LLM reasoning abilities which requires us to fundamentally rethink the impact of RL training in reasoning LLMs and the need of a better paradigm. Project Page: https://limit-of-RLVR.github.io

Learning from Demonstration (LfD) aims to facilitate rapid Reinforcement Learning (RL) by leveraging expert demonstrations to pre-train the RL agent. However, the limited availability of expert demonstration data often hinders its ability to effectively aid downstream RL learning. To address this problem, we propose a novel two-stage method dubbed as Skill-enhanced Reinforcement Learning Acceleration (SeRLA). SeRLA introduces a skill-level adversarial Positive-Unlabeled (PU) learning model to extract useful skill prior knowledge by enabling learning from both limited expert data and general low-cost demonstration data in the offline prior learning stage. Subsequently, it deploys a skill-based soft actor-critic algorithm to leverage this acquired prior knowledge in the downstream online RL stage for efficient training of a skill policy network. Moreover, we develop a simple skill-level data enhancement technique to further alleviate data sparsity and improve both skill prior learning and downstream skill policy training. Our experimental results on multiple standard RL environments show the proposed SeRLA method achieves state-of-the-art performance on accelerating reinforcement learning on downstream tasks, especially in the early learning phase.

Recent advances in test-time scaling have led to the emergence of thinking LLMs that exhibit self-reflective behaviors and multi-step reasoning. While RL drives this self-improvement paradigm, a recent study (Gandhi et al., 2025) shows that RL alone does not truly instill these new reasoning abilities - it merely draws out behaviors already present in the base models. This raises a question: How can we train the models that don't exhibit such thinking behavior to develop it in the first place? To this end, we propose ThinkTuning, a GRPO-based interactive training approach where we augment the rollouts of a student model with the guidance from a teacher model. A simple idea from classroom practice inspires our method: a teacher poses a problem, lets the student try an answer, then gives corrective feedback -- enough to point the mind in the right direction and then show the solution. Each piece of feedback reshapes the student's thoughts, leading them to arrive at the correct solution. Similarly, we find that this type of implicit supervision through feedback from a teacher model of the same size improves the reasoning capabilities of the student model. In particular, on average, our method shows a 3.85% improvement over zero-shot baselines across benchmarks, and on MATH-500, AIME and GPQA-Diamond it shows 2.08%, 2.23% and 3.99% improvements over the vanilla-GRPO baseline. Source code is available at https://github.com/3rdAT/ThinkTuning.

Large Language Models (LLMs) have shown substantial advances through reinforcement learning (RL), particularly in domains where rewards can be programmatically verified, such as mathematics and code. In these areas, models benefit from a well-defined operational base guided by explicit rule-based objectives. However, this progress reveals a significant limitation: in open-ended domains where rewards are ambiguous, subjective, or context-dependent, such as creative writing, scientific reasoning, and notably medical consultation, robust reward functions are lacking, making these areas challenging for current RL strategies. To bridge this gap, we introduce ORBIT, an open-ended rubric-based incremental training framework specifically designed for high-stakes medical dialogue. ORBIT integrates syn- thetic dialogue generation with the dynamic creation of rubrics, employing these rubrics to direct an incremental RL process. In particular, this approach does not depend on external medical knowledge or manual rules, instead utilizing rubric-guided feedback to shape learning. When implemented on the Qwen3-4B-Instruct model, our method can greatly enhance its performance on the HealthBench-Hard benchmark from 7.0 to 27.2 using only 2k samples, thus achieving state-of-the-art results for models of this scale. Our analysis confirms that rubric-driven RL fos-ters consistent performance gains across diverse consultation scenarios, going beyond simple numerical improvements. These findings underscore rubric-based feedback as a scalable strategy for advancing LLMs in intricate, open-ended tasks.

Reinforcement learning (RL) has recently shown strong potential in improving the reasoning capabilities of large language models and is now being actively extended to vision-language models (VLMs). However, existing RL applications in VLMs often rely on heavily engineered frameworks that hinder reproducibility and accessibility, while lacking standardized evaluation protocols, making it difficult to compare results or interpret training dynamics. This work introduces a transparent, from-scratch framework for RL in VLMs, offering a minimal yet functional four-step pipeline validated across multiple models and datasets. In addition, a standardized evaluation scheme is proposed to assess training dynamics and reflective behaviors. Extensive experiments on visual reasoning tasks uncover key empirical findings: response length is sensitive to random seeds, reflection correlates with output length, and RL consistently outperforms supervised fine-tuning (SFT) in generalization, even with high-quality data. These findings, together with the proposed framework, aim to establish a reproducible baseline and support broader engagement in RL-based VLM research.

Reinforcement Learning with Verifiable Rewards (RLVR) has emerged as a key ingredient for unlocking complex reasoning capabilities in large language models. Recent work ProRL has shown promise in scaling RL by increasing the number of training steps. However, performance plateaus after thousands of steps, with clear diminishing returns from allocating more computation to additional training. In this work, we investigate a complementary paradigm for scaling RL, BroR-Lincreasing the number of rollouts per example to hundreds to exhaustively Broaden exploration, which yields continuous performance gains beyond the saturation point observed in ProRL when scaling the number of training steps. Our approach is motivated by a mass balance equation analysis allowing us to characterize the rate of change in probability mass for correct and incorrect tokens during the reinforcement process. We show that under a one-step RL assumption, sampled rollout tokens always contribute to correct-mass expansion, while unsampled tokens outside rollouts may lead to gains or losses depending on their distribution and the net reward balance. Importantly, as the number of rollouts per example N increases, the effect of unsampled terms diminishes, ensuring overall correct-mass expansion. To validate our theoretical analysis, we conduct simulations under more relaxed conditions and find that a sufficiently large rollout size N-corresponding to ample exploration-guarantees an increase in the probability mass of all correct tokens. Empirically, BroRL revives models saturated after 3K ProRL training steps and demonstrates robust, continuous improvement, achieving state-of-the-art results for the 1.5B model across diverse benchmarks.

Reinforcement learning (RL) has become the dominant paradigm for endowing language models with advanced reasoning capabilities. Despite the substantial empirical gains demonstrated by RL-based training methods like GRPO, a granular understanding of their advantages is still lacking. To address this gap, we introduce a fine-grained analytic framework to dissect the impact of RL on reasoning. Our framework specifically investigates key elements that have been hypothesized to benefit from RL training: (1) plan-following and execution, (2) problem decomposition, and (3) improved reasoning and knowledge utilization. Using this framework, we gain insights beyond mere accuracy. For instance, providing models with explicit step-by-step plans surprisingly degrades performance on the most challenging benchmarks, yet RL-tuned models exhibit greater robustness, experiencing markedly smaller performance drops than their base counterparts. This suggests that RL may not primarily enhance the execution of external plans but rather empower models to formulate and follow internal strategies better suited to their reasoning processes. Conversely, we observe that RL enhances the model's capacity to integrate provided knowledge into its reasoning process, leading to performance improvements across diverse tasks. We also study difficulty, showing improved training by developing new ways to exploit hard problems. Our findings lay a foundation for more principled training and evaluation of reasoning models.

End-to-end autonomous driving models trained solely with imitation learning (IL) often suffer from poor generalization. In contrast, reinforcement learning (RL) promotes exploration through reward maximization but faces challenges such as sample inefficiency and unstable convergence. A natural solution is to combine IL and RL. Moving beyond the conventional two-stage paradigm (IL pretraining followed by RL fine-tuning), we propose CoIRL-AD, a competitive dual-policy framework that enables IL and RL agents to interact during training. CoIRL-AD introduces a competition-based mechanism that facilitates knowledge exchange while preventing gradient conflicts. Experiments on the nuScenes dataset show an 18% reduction in collision rate compared to baselines, along with stronger generalization and improved performance on long-tail scenarios. Code is available at: https://github.com/SEU-zxj/CoIRL-AD.

Reinforcement learning (RL) with verifiable rewards (RLVR) has shown promising results in mathematical reasoning and coding tasks where well-structured reference answers are available. However, its applicability to broader domains remains underexplored. In this work, we study the extension of RLVR to more diverse domains such as medicine, chemistry, psychology, and economics. We observe high agreement in binary judgments across different large language models (LLMs) when objective reference answers exist, which challenges the necessity of large-scale annotation for training domain-specific reward models. To address the limitations of binary rewards when handling unstructured reference answers, we further incorporate model-based soft scoring into RLVR to improve its flexibility. Our experiments show that a distilled generative reward model can serve as an effective cross-domain verifier, providing reliable reward signals for RL without requiring domain-specific annotations. By fine-tuning a base 7B model using various RL algorithms against our reward model, we obtain policies that outperform state-of-the-art open-source aligned LLMs such as Qwen2.5-72B-Instruct and DeepSeek-R1-Distill-Qwen-32B by a large margin, across domains in free-form answer settings. This also strengthens RLVR's robustness and scalability, highlighting its potential for real-world applications with noisy or weak labels.

Despite the promise of RLHF in aligning LLMs with human preferences, it often leads to superficial alignment, prioritizing stylistic changes over improving downstream performance of LLMs. Underspecified preferences could obscure directions to align the models. Lacking exploration restricts identification of desirable outputs to improve the models. To overcome these challenges, we propose a novel framework: Reinforcement Learning from Reflective Feedback (RLRF), which leverages fine-grained feedback based on detailed criteria to improve the core capabilities of LLMs. RLRF employs a self-reflection mechanism to systematically explore and refine LLM responses, then fine-tuning the models via a RL algorithm along with promising responses. Our experiments across Just-Eval, Factuality, and Mathematical Reasoning demonstrate the efficacy and transformative potential of RLRF beyond superficial surface-level adjustment.

In this paper, we survey recent advances in Reinforcement Learning (RL) for reasoning with Large Language Models (LLMs). RL has achieved remarkable success in advancing the frontier of LLM capabilities, particularly in addressing complex logical tasks such as mathematics and coding. As a result, RL has emerged as a foundational methodology for transforming LLMs into LRMs. With the rapid progress of the field, further scaling of RL for LRMs now faces foundational challenges not only in computational resources but also in algorithm design, training data, and infrastructure. To this end, it is timely to revisit the development of this domain, reassess its trajectory, and explore strategies to enhance the scalability of RL toward Artificial SuperIntelligence (ASI). In particular, we examine research applying RL to LLMs and LRMs for reasoning abilities, especially since the release of DeepSeek-R1, including foundational components, core problems, training resources, and downstream applications, to identify future opportunities and directions for this rapidly evolving area. We hope this review will promote future research on RL for broader reasoning models. Github: https://github.com/TsinghuaC3I/Awesome-RL-for-LRMs

Reinforcement learning with verifiable rewards (RLVR) has delivered impressive gains in mathematical and multimodal reasoning and has become a standard post-training paradigm for contemporary language and vision-language models. However, the RLVR recipe introduces a significant risk of capability regression, where models forget foundational skills after prolonged training without employing regularization strategies. We empirically confirm this concern, observing that open-source reasoning models suffer performance degradation on core capabilities such as perception and faithfulness. While imposing regularization terms like KL divergence can help prevent deviation from the base model, these terms are calculated on the current task, thus they do not guarantee broader knowledge. Meanwhile, commonly used experience replay across heterogeneous domains makes it nontrivial to decide how much training focus each objective should receive. To address this, we propose RECAP-a replay strategy with dynamic objective reweighting for general knowledge preservation. Our reweighting mechanism adapts in an online manner using short-horizon signals of convergence and instability, shifting the post-training focus away from saturated objectives and toward underperforming or volatile ones. Our method is end-to-end and readily applicable to existing RLVR pipelines without training additional models or heavy tuning. Extensive experiments on benchmarks based on Qwen2.5-VL-3B and Qwen2.5-VL-7B demonstrate the effectiveness of our method, which not only preserves general capabilities but also improves reasoning by enabling more flexible trade-offs among in-task rewards.

Reinforcement learning (RL) has significantly improved the reasoning ability of large language models. However, current reward models underperform in challenging reasoning scenarios and predominant RL training paradigms rely on rule-based or reference-based rewards, which impose two critical limitations: 1) the dependence on finely annotated reference answer to attain rewards; and 2) the requirement for constrained output format. These limitations fundamentally hinder further RL data scaling and sustained enhancement of model reasoning performance. To address these limitations, we propose a comprehensive framework for evaluating and improving the performance of reward models in complex reasoning scenarios. We first present a reasoning-oriented benchmark (Libra Bench), systematically constructed from a diverse collection of challenging mathematical problems and advanced reasoning models, to address the limitations of existing reward model benchmarks in reasoning scenarios. We further introduce a novel approach for improving the generative reward model via learning-to-think methodologies. Based on the proposed approach, we develop Libra-RM series, a collection of generative reward models with reasoning capabilities that achieve state-of-the-art results on various benchmarks. Comprehensive downstream experiments are conducted and the experimental results demonstrate the correlation between our Libra Bench and downstream application, and the potential of Libra-RM to further improve reasoning models with unlabeled data.

A promising approach for improving reasoning in large language models is to use process reward models (PRMs). PRMs provide feedback at each step of a multi-step reasoning trace, potentially improving credit assignment over outcome reward models (ORMs) that only provide feedback at the final step. However, collecting dense, per-step human labels is not scalable, and training PRMs from automatically-labeled data has thus far led to limited gains. To improve a base policy by running search against a PRM or using it as dense rewards for reinforcement learning (RL), we ask: "How should we design process rewards?". Our key insight is that, to be effective, the process reward for a step should measure progress: a change in the likelihood of producing a correct response in the future, before and after taking the step, corresponding to the notion of step-level advantages in RL. Crucially, this progress should be measured under a prover policy distinct from the base policy. We theoretically characterize the set of good provers and our results show that optimizing process rewards from such provers improves exploration during test-time search and online RL. In fact, our characterization shows that weak prover policies can substantially improve a stronger base policy, which we also observe empirically. We validate our claims by training process advantage verifiers (PAVs) to predict progress under such provers, and show that compared to ORMs, test-time search against PAVs is >8% more accurate, and 1.5-5times more compute-efficient. Online RL with dense rewards from PAVs enables one of the first results with 5-6times gain in sample efficiency, and >6% gain in accuracy, over ORMs.

Real-world reinforcement learning (RL) is often severely limited since typical RL algorithms heavily rely on the reset mechanism to sample proper initial states. In practice, the reset mechanism is expensive to implement due to the need for human intervention or heavily engineered environments. To make learning more practical, we propose a generic no-regret reduction to systematically design reset-free RL algorithms. Our reduction turns reset-free RL into a two-player game. We show that achieving sublinear regret in this two-player game would imply learning a policy that has both sublinear performance regret and sublinear total number of resets in the original RL problem. This means that the agent eventually learns to perform optimally and avoid resets. By this reduction, we design an instantiation for linear Markov decision processes, which is the first provably correct reset-free RL algorithm to our knowledge.

The combination of Reinforcement Learning (RL) with deep learning has led to a series of impressive feats, with many believing (deep) RL provides a path towards generally capable agents. However, the success of RL agents is often highly sensitive to design choices in the training process, which may require tedious and error-prone manual tuning. This makes it challenging to use RL for new problems, while also limits its full potential. In many other areas of machine learning, AutoML has shown it is possible to automate such design choices and has also yielded promising initial results when applied to RL. However, Automated Reinforcement Learning (AutoRL) involves not only standard applications of AutoML but also includes additional challenges unique to RL, that naturally produce a different set of methods. As such, AutoRL has been emerging as an important area of research in RL, providing promise in a variety of applications from RNA design to playing games such as Go. Given the diversity of methods and environments considered in RL, much of the research has been conducted in distinct subfields, ranging from meta-learning to evolution. In this survey we seek to unify the field of AutoRL, we provide a common taxonomy, discuss each area in detail and pose open problems which would be of interest to researchers going forward.

The integration of reinforcement learning (RL) into the reasoning capabilities of Multimodal Large Language Models (MLLMs) has rapidly emerged as a transformative research direction. While MLLMs significantly extend Large Language Models (LLMs) to handle diverse modalities such as vision, audio, and video, enabling robust reasoning across multimodal inputs remains a major challenge. This survey systematically reviews recent advances in RL-based reasoning for MLLMs, covering key algorithmic designs, reward mechanism innovations, and practical applications. We highlight two main RL paradigms--value-free and value-based methods--and analyze how RL enhances reasoning abilities by optimizing reasoning trajectories and aligning multimodal information. Furthermore, we provide an extensive overview of benchmark datasets, evaluation protocols, and existing limitations, and propose future research directions to address current bottlenecks such as sparse rewards, inefficient cross-modal reasoning, and real-world deployment constraints. Our goal is to offer a comprehensive and structured guide to researchers interested in advancing RL-based reasoning in the multimodal era.

Reinforcement learning (RL) has been widely used in text generation to alleviate the exposure bias issue or to utilize non-parallel datasets. The reward function plays an important role in making RL training successful. However, previous reward functions are typically task-specific and sparse, restricting the use of RL. In our work, we propose a task-agnostic approach that derives a step-wise reward function directly from a model trained with teacher forcing. We additionally propose a simple modification to stabilize the RL training on non-parallel datasets with our induced reward function. Empirical results show that our method outperforms self-training and reward regression methods on several text generation tasks, confirming the effectiveness of our reward function.

Search agents powered by Large Language Models (LLMs) have demonstrated significant potential in tackling knowledge-intensive tasks. Reinforcement learning (RL) has emerged as a powerful paradigm for training these agents to perform complex, multi-step reasoning. However, prior RL-based methods often rely on sparse or rule-based rewards, which can lead agents to commit to suboptimal or erroneous reasoning paths without the ability to recover. To address these limitations, we propose ReSeek, a novel self-correcting framework for training search agents. Our framework introduces a self-correction mechanism that empowers the agent to dynamically identify and recover from erroneous search paths during an episode. By invoking a special JUDGE action, the agent can judge the information and re-plan its search strategy. To guide this process, we design a dense, instructive process reward function, which decomposes into a correctness reward for retrieving factual information and a utility reward for finding information genuinely useful for the query. Furthermore, to mitigate the risk of data contamination in existing datasets, we introduce FictionalHot, a new and challenging benchmark with recently curated questions requiring complex reasoning. Being intuitively reasonable and practically simple, extensive experiments show that agents trained with ReSeek significantly outperform SOTA baselines in task success rate and path faithfulness.

Reinforcement learning with AI feedback (RLAIF) is a popular paradigm for improving the instruction-following abilities of powerful pre-trained language models. RLAIF first performs supervised fine-tuning (SFT) using demonstrations from a teacher model and then further fine-tunes the model with reinforcement learning (RL), using feedback from a critic model. While recent popular open-source models have demonstrated substantial improvements in performance from the RL step, in this paper we question whether the complexity of this RL step is truly warranted for AI feedback. We show that the improvements of the RL step are virtually entirely due to the widespread practice of using a weaker teacher model (e.g. GPT-3.5) for SFT data collection than the critic (e.g., GPT-4) used for AI feedback generation. Specifically, we show that simple supervised fine-tuning with GPT-4 as the teacher outperforms existing RLAIF pipelines. More generally, we find that the gains from RLAIF vary substantially across base model families, test-time evaluation protocols, and critic models. Finally, we provide a mechanistic explanation for when SFT may outperform the full two-step RLAIF pipeline as well as suggestions for making RLAIF maximally useful in practice.

This paper presents our work on the Light-R1 series, with models, data, and code all released. We first focus on training long COT models from scratch, specifically starting from models initially lacking long COT capabilities. Using a curriculum training recipe consisting of two-stage SFT and semi-on-policy DPO, we train our model Light-R1-32B from Qwen2.5-32B-Instruct, resulting in superior math performance compared to DeepSeek-R1-Distill-Qwen-32B. Despite being trained exclusively on math data, Light-R1-32B shows strong generalization across other domains. In the subsequent phase of this work, we highlight the significant benefit of the 3k dataset constructed for the second SFT stage on enhancing other models. By fine-tuning DeepSeek-R1-Distilled models using this dataset, we obtain new SOTA models in 7B and 14B, while the 32B model, Light-R1-32B-DS performed comparably to QwQ-32B and DeepSeek-R1. Furthermore, we extend our work by applying reinforcement learning, specifically GRPO, on long-COT models to further improve reasoning performance. We successfully train our final Light-R1-14B-DS with RL, achieving SOTA performance among 14B parameter models in math. With AIME24 & 25 scores of 74.0 and 60.2 respectively, Light-R1-14B-DS surpasses even many 32B models and DeepSeek-R1-Distill-Llama-70B. Its RL training also exhibits well expected behavior, showing simultaneous increase in response length and reward score. The Light-R1 series of work validates training long-COT models from scratch, showcases the art in SFT data and releases SOTA models from RL.

Past analyses of reinforcement learning from human feedback (RLHF) assume that the human fully observes the environment. What happens when human feedback is based only on partial observations? We formally define two failure cases: deception and overjustification. Modeling the human as Boltzmann-rational w.r.t. a belief over trajectories, we prove conditions under which RLHF is guaranteed to result in policies that deceptively inflate their performance, overjustify their behavior to make an impression, or both. To help address these issues, we mathematically characterize how partial observability of the environment translates into (lack of) ambiguity in the learned return function. In some cases, accounting for partial observability makes it theoretically possible to recover the return function and thus the optimal policy, while in other cases, there is irreducible ambiguity. We caution against blindly applying RLHF in partially observable settings and propose research directions to help tackle these challenges.

While recent advances have boosted LM proficiency in linguistic benchmarks, LMs consistently struggle to reason correctly on complex tasks like mathematics. We turn to Reinforcement Learning from Human Feedback (RLHF) as a method with which to shape model reasoning processes. In particular, we explore two reward schemes, outcome-supervised reward models (ORMs) and process-supervised reward models (PRMs), to optimize for logical reasoning. Our results show that the fine-grained reward provided by PRM-based methods enhances accuracy on simple mathematical reasoning (GSM8K) while, unexpectedly, reducing performance in complex tasks (MATH). Furthermore, we show the critical role reward aggregation functions play in model performance. Providing promising avenues for future research, our study underscores the need for further exploration into fine-grained reward modeling for more reliable language models.

Recent advances in large reasoning models highlight Reinforcement Learning with Verifiable Rewards (RLVR) as a promising method for enhancing AI's capabilities, particularly in solving complex logical tasks. However, it remains unclear whether RLVR truly expands a model's reasoning boundary or merely amplifies high-reward outputs that the base model already knows for improved precision. This study presents a theoretical and empirical investigation that provides fresh insights into the potential limits of RLVR. First, we offer a new theoretical perspective that RLVR is constrained by the base model's support-unable to sample solutions with zero initial probability-and operates as a conservative reweighting mechanism that may restrict the discovery of entirely original solutions. We also identify an entropy-reward tradeoff: while RLVR reliably enhances precision, it may progressively narrow exploration and potentially overlook correct yet underrepresented solutions. Extensive empirical experiments validate that while RLVR consistently improves pass@1, the shrinkage of empirical support generally outweighs the expansion of empirical support under larger sampling budgets, failing to recover correct answers that were previously accessible to the base model. Interestingly, we also observe that while RLVR sometimes increases token-level entropy, resulting in greater uncertainty at each generation step, answer-level entropy declines, indicating that these seemingly more uncertain paths ultimately converge onto a smaller set of distinct answers. Taken together, these findings reveal potential limits of RLVR in extending reasoning horizons. Breaking this invisible leash may require future algorithmic innovations such as explicit exploration mechanisms or hybrid strategies that seed probability mass into underrepresented solution regions.

Recent AI advancements, such as OpenAI's new models, are transforming LLMs into LRMs (Large Reasoning Models) that perform reasoning during inference, taking extra time and compute for higher-quality outputs. We aim to uncover the algorithmic framework for training LRMs. Methods like self-consistency, PRM, and AlphaZero suggest reasoning as guided search. We ask: what is the simplest, most scalable way to enable search in LLMs? We propose a post-training framework called Reinforcement Learning via Self-Play (RLSP). RLSP involves three steps: (1) supervised fine-tuning with human or synthetic demonstrations of the reasoning process, (2) using an exploration reward signal to encourage diverse and efficient reasoning behaviors, and (3) RL training with an outcome verifier to ensure correctness while preventing reward hacking. Our key innovation is to decouple exploration and correctness signals during PPO training, carefully balancing them to improve performance and efficiency. Empirical studies in the math domain show that RLSP improves reasoning. On the Llama-3.1-8B-Instruct model, RLSP can boost performance by 23% in MATH-500 test set; On AIME 2024 math problems, Qwen2.5-32B-Instruct improved by 10% due to RLSP. However, a more important finding of this work is that the models trained using RLSP, even with the simplest exploration reward that encourages the model to take more intermediate steps, showed several emergent behaviors such as backtracking, exploration of ideas, and verification. These findings demonstrate that RLSP framework might be enough to enable emergence of complex reasoning abilities in LLMs when scaled. Lastly, we propose a theory as to why RLSP search strategy is more suitable for LLMs inspired by a remarkable result that says CoT provably increases computational power of LLMs, which grows as the number of steps in CoT li2024chain,merrill2023expresssive.

From a first-principles perspective, it may seem odd that the strongest results in foundation model fine-tuning (FT) are achieved via a relatively complex, two-stage training procedure. Specifically, one first trains a reward model (RM) on some dataset (e.g. human preferences) before using it to provide online feedback as part of a downstream reinforcement learning (RL) procedure, rather than directly optimizing the policy parameters on the dataset via offline maximum likelihood estimation. In fact, from an information-theoretic perspective, we can only lose information via passing through a reward model and cannot create any new information via on-policy sampling. To explain this discrepancy, we scrutinize several hypotheses on the value of RL in FT through both theoretical and empirical lenses. Of the hypotheses considered, we find the most support for the explanation that on problems with a generation-verification gap, the combination of the ease of learning the relatively simple RM (verifier) from the preference data, coupled with the ability of the downstream RL procedure to then filter its search space to the subset of policies (generators) that are optimal for relatively simple verifiers is what leads to the superior performance of online FT.

Inspired by the success of DeepSeek-R1, we explore the potential of rule-based reinforcement learning (RL) in MLLM post-training for perception policy learning. While promising, our initial experiments reveal that incorporating a thinking process through RL does not consistently lead to performance gains across all visual perception tasks. This leads us to delve into the essential role of RL in the context of visual perception. In this work, we return to the fundamentals and explore the effects of RL on different perception tasks. We observe that the perceptual complexity is a major factor in determining the effectiveness of RL. We also observe that reward design plays a crucial role in further approching the upper limit of model perception. To leverage these findings, we propose Perception-R1, a scalable RL framework using GRPO during MLLM post-training. With a standard Qwen2.5-VL-3B-Instruct, Perception-R1 achieves +4.2% on RefCOCO+, +17.9% on PixMo-Count, +4.2% on PageOCR, and notably, 31.9% AP on COCO2017 val for the first time, establishing a strong baseline for perception policy learning.

Current reinforcement learning (RL) frameworks for large language models (LLM) post-training typically assume a fixed prompt distribution, which is sub-optimal and bottlenecks scalability. Prior works have explored prompt evolving, but are often limited to the supervised fine-tuning stage, and prompts are sampled and evolved uniformly without signals. This empirical work presents a paradigm shift: Evolving Alignment via Asymmetric Self-Play (eva), that casts post-training as an infinite game with regret-based signals for 2 players: (i) a creator, who strategically samples and creates new informative prompts and (ii) a solver, who learns to produce preferred responses. eva is the first method that allows language models to adaptively create training prompts in both offline and online RL post-training. The design is simple, easy-to-use yet remarkably effective: eva sets a new SOTA on challenging benchmarks, without any extra human prompts, e.g. it boosts the win-rate of gemma-2-9b-it on Arena-Hard by 51.6% -> 60.1% for DPO and 52.6% -> 62.4% for RLOO, surpassing claude-3-opus and catching up to gemini-1.5-pro, both of which are orders of magnitude larger. Extensive experiments show eva can create effective RL curricula and is robust across ablations. We believe adaptively evolving prompts are key to designing the next-generation RL post-training scheme.

Reinforcement learning (RL) solves sequential decision-making problems via a trial-and-error process interacting with the environment. While RL achieves outstanding success in playing complex video games that allow huge trial-and-error, making errors is always undesired in the real world. To improve the sample efficiency and thus reduce the errors, model-based reinforcement learning (MBRL) is believed to be a promising direction, which builds environment models in which the trial-and-errors can take place without real costs. In this survey, we take a review of MBRL with a focus on the recent progress in deep RL. For non-tabular environments, there is always a generalization error between the learned environment model and the real environment. As such, it is of great importance to analyze the discrepancy between policy training in the environment model and that in the real environment, which in turn guides the algorithm design for better model learning, model usage, and policy training. Besides, we also discuss the recent advances of model-based techniques in other forms of RL, including offline RL, goal-conditioned RL, multi-agent RL, and meta-RL. Moreover, we discuss the applicability and advantages of MBRL in real-world tasks. Finally, we end this survey by discussing the promising prospects for the future development of MBRL. We think that MBRL has great potential and advantages in real-world applications that were overlooked, and we hope this survey could attract more research on MBRL.

Recently DeepSeek R1 demonstrated how reinforcement learning with simple rule-based incentives can enable autonomous development of complex reasoning in large language models, characterized by the "aha moment", in which the model manifest self-reflection and increased response length during training. However, attempts to extend this success to multimodal reasoning often failed to reproduce these key characteristics. In this report, we present the first successful replication of these emergent characteristics for multimodal reasoning on only a non-SFT 2B model. Starting with Qwen2-VL-2B and applying reinforcement learning directly on the SAT dataset, our model achieves 59.47% accuracy on CVBench, outperforming the base model by approximately ~30% and exceeding both SFT setting by ~2%. In addition, we share our failed attempts and insights in attempting to achieve R1-like reasoning using RL with instruct models. aiming to shed light on the challenges involved. Our key observations include: (1) applying RL on instruct model often results in trivial reasoning trajectories, and (2) naive length reward are ineffective in eliciting reasoning capabilities. The project code is available at https://github.com/turningpoint-ai/VisualThinker-R1-Zero

Reinforcement learning (RL)-based fine-tuning has become a crucial step in post-training language models for advanced mathematical reasoning and coding. Following the success of frontier reasoning models, recent work has demonstrated that RL fine-tuning consistently improves performance, even in smaller-scale models; however, the underlying mechanisms driving these improvements are not well-understood. Understanding the effects of RL fine-tuning requires disentangling its interaction with pretraining data composition, hyperparameters, and model scale, but such problems are exacerbated by the lack of transparency regarding the training data used in many existing models. In this work, we present a systematic end-to-end study of RL fine-tuning for mathematical reasoning by training models entirely from scratch on different mixtures of fully open datasets. We investigate the effects of various RL fine-tuning algorithms (PPO, GRPO, and Expert Iteration) across models of different scales. Our study reveals that RL algorithms consistently converge towards a dominant output distribution, amplifying patterns in the pretraining data. We also find that models of different scales trained on the same data mixture will converge to distinct output distributions, suggesting that there are scale-dependent biases in model generalization. Moreover, we find that RL post-training on simpler questions can lead to performance gains on harder ones, indicating that certain reasoning capabilities generalize across tasks. Our findings show that small-scale proxies in controlled settings can elicit interesting insights regarding the role of RL in shaping language model behavior.

Reinforcement learning with verifiable rewards (RLVR) is a practical and scalable approach to enhancing large language models in areas such as math, code, and other structured tasks. Two questions motivate this paper: how much of the reported gains survive under strictly parity-controlled evaluation, and whether RLVR is cost-free or exacts a measurable tax. We argue that progress is real, but gains are often overstated due to three forces - an RLVR tax, evaluation pitfalls, and data contamination. Using a partial-prompt contamination audit and matched-budget reproductions across base and RL models, we show that several headline gaps shrink or vanish under clean, parity-controlled evaluation. We then propose a tax-aware training and evaluation protocol that co-optimizes accuracy, grounding, and calibrated abstention and standardizes budgeting and provenance checks. Applied to recent RLVR setups, this protocol yields more reliable estimates of reasoning gains and, in several cases, revises prior conclusions. Our position is constructive: RLVR is valuable and industry-ready; we advocate keeping its practical benefits while prioritizing reliability, safety, and measurement.

We provide a theoretical framework for Reinforcement Learning with Human Feedback (RLHF). Our analysis shows that when the true reward function is linear, the widely used maximum likelihood estimator (MLE) converges under both the Bradley-Terry-Luce (BTL) model and the Plackett-Luce (PL) model. However, we show that when training a policy based on the learned reward model, MLE fails while a pessimistic MLE provides policies with improved performance under certain coverage assumptions. Additionally, we demonstrate that under the PL model, the true MLE and an alternative MLE that splits the K-wise comparison into pairwise comparisons both converge. Moreover, the true MLE is asymptotically more efficient. Our results validate the empirical success of existing RLHF algorithms in InstructGPT and provide new insights for algorithm design. Furthermore, our results unify the problem of RLHF and max-entropy Inverse Reinforcement Learning (IRL), and provide the first sample complexity bound for max-entropy IRL.

Reinforcement learning (RL) has emerged as a powerful approach for tackling complex problems. The recent introduction of multi-objective reinforcement learning (MORL) has further expanded the scope of RL by enabling agents to make trade-offs among multiple objectives. This advancement not only has broadened the range of problems that can be tackled but also created numerous opportunities for exploration and advancement. Yet, the effectiveness of RL agents heavily relies on appropriately setting their hyperparameters. In practice, this task often proves to be challenging, leading to unsuccessful deployments of these techniques in various instances. Hence, prior research has explored hyperparameter optimization in RL to address this concern. This paper presents an initial investigation into the challenge of hyperparameter optimization specifically for MORL. We formalize the problem, highlight its distinctive challenges, and propose a systematic methodology to address it. The proposed methodology is applied to a well-known environment using a state-of-the-art MORL algorithm, and preliminary results are reported. Our findings indicate that the proposed methodology can effectively provide hyperparameter configurations that significantly enhance the performance of MORL agents. Furthermore, this study identifies various future research opportunities to further advance the field of hyperparameter optimization for MORL.

Model-based reinforcement learning (MBRL) has been shown to be a powerful framework for data-efficiently learning control of continuous tasks. Recent work in MBRL has mostly focused on using more advanced function approximators and planning schemes, with little development of the general framework. In this paper, we identify a fundamental issue of the standard MBRL framework -- what we call the objective mismatch issue. Objective mismatch arises when one objective is optimized in the hope that a second, often uncorrelated, metric will also be optimized. In the context of MBRL, we characterize the objective mismatch between training the forward dynamics model w.r.t.~the likelihood of the one-step ahead prediction, and the overall goal of improving performance on a downstream control task. For example, this issue can emerge with the realization that dynamics models effective for a specific task do not necessarily need to be globally accurate, and vice versa globally accurate models might not be sufficiently accurate locally to obtain good control performance on a specific task. In our experiments, we study this objective mismatch issue and demonstrate that the likelihood of one-step ahead predictions is not always correlated with control performance. This observation highlights a critical limitation in the MBRL framework which will require further research to be fully understood and addressed. We propose an initial method to mitigate the mismatch issue by re-weighting dynamics model training. Building on it, we conclude with a discussion about other potential directions of research for addressing this issue.

Recent studies generally enhance MLLMs' reasoning capabilities via supervised fine-tuning on high-quality chain-of-thought reasoning data, which often leads models to merely imitate successful reasoning paths without understanding what the wrong reasoning paths are. In this work, we aim to enhance the MLLMs' reasoning ability beyond passively imitating positive reasoning paths. To this end, we design Step-wise Group Relative Policy Optimization (StepGRPO), a new online reinforcement learning framework that enables MLLMs to self-improve reasoning ability via simple, effective and dense step-wise rewarding. Specifically, StepGRPO introduces two novel rule-based reasoning rewards: Step-wise Reasoning Accuracy Reward (StepRAR) and Step-wise Reasoning Validity Reward (StepRVR). StepRAR rewards the reasoning paths that contain necessary intermediate reasoning steps via a soft key-step matching technique, while StepRAR rewards reasoning paths that follow a well-structured and logically consistent reasoning process through a reasoning completeness and logic evaluation strategy. With the proposed StepGRPO, we introduce R1-VL, a series of MLLMs with outstanding capabilities in step-by-step reasoning. Extensive experiments over 8 benchmarks demonstrate the superiority of our methods.

Classification is a core task in machine learning. Recent research has shown that although Multimodal Large Language Models (MLLMs) are initially poor at image classification, fine-tuning them with an adequate amount of data can significantly enhance their performance, making them comparable to SOTA classification models. However, acquiring large-scale labeled data is expensive. In this paper, we explore few-shot MLLM classification fine-tuning. We found that SFT can cause severe overfitting issues and may even degrade performance over the zero-shot approach. To address this challenge, inspired by the recent successes in rule-based reinforcement learning, we propose CLS-RL, which uses verifiable signals as reward to fine-tune MLLMs. We discovered that CLS-RL outperforms SFT in most datasets and has a much higher average accuracy on both base-to-new and few-shot learning setting. Moreover, we observed a free-lunch phenomenon for CLS-RL; when models are fine-tuned on a particular dataset, their performance on other distinct datasets may also improve over zero-shot models, even if those datasets differ in distribution and class names. This suggests that RL-based methods effectively teach models the fundamentals of classification. Lastly, inspired by recent works in inference time thinking, we re-examine the `thinking process' during fine-tuning, a critical aspect of RL-based methods, in the context of visual classification. We question whether such tasks require extensive thinking process during fine-tuning, proposing that this may actually detract from performance. Based on this premise, we introduce the No-Thinking-CLS-RL method, which minimizes thinking processes during training by setting an equality accuracy reward. Our findings indicate that, with much less fine-tuning time, No-Thinking-CLS-RL method achieves superior in-domain performance and generalization capabilities than CLS-RL.

Reinforcement learning (RL) is frequently employed in fine-tuning large language models (LMs), such as GPT-3, to penalize them for undesirable features of generated sequences, such as offensiveness, social bias, harmfulness or falsehood. The RL formulation involves treating the LM as a policy and updating it to maximise the expected value of a reward function which captures human preferences, such as non-offensiveness. In this paper, we analyze challenges associated with treating a language model as an RL policy and show how avoiding those challenges requires moving beyond the RL paradigm. We start by observing that the standard RL approach is flawed as an objective for fine-tuning LMs because it leads to distribution collapse: turning the LM into a degenerate distribution. Then, we analyze KL-regularised RL, a widely used recipe for fine-tuning LMs, which additionally constrains the fine-tuned LM to stay close to its original distribution in terms of Kullback-Leibler (KL) divergence. We show that KL-regularised RL is equivalent to variational inference: approximating a Bayesian posterior which specifies how to update a prior LM to conform with evidence provided by the reward function. We argue that this Bayesian inference view of KL-regularised RL is more insightful than the typically employed RL perspective. The Bayesian inference view explains how KL-regularised RL avoids the distribution collapse problem and offers a first-principles derivation for its objective. While this objective happens to be equivalent to RL (with a particular choice of parametric reward), there exist other objectives for fine-tuning LMs which are no longer equivalent to RL. That observation leads to a more general point: RL is not an adequate formal framework for problems such as fine-tuning language models. These problems are best viewed as Bayesian inference: approximating a pre-defined target distribution.

Reinforcement Learning with Human Feedback (RLHF) has achieved great success in aligning large language models (LLMs) with human preferences. Prevalent RLHF approaches are reward-based, following the Bradley-Terry (BT) model assumption, which may not fully capture the complexity of human preferences. In this paper, we explore RLHF under a general preference framework and approach it from a game-theoretic perspective. Specifically, we formulate the problem as a two-player game and propose a novel algorithm, iterative Nash policy optimization (INPO). The key idea is to let the policy play against itself via no-regret learning, thereby approximating the Nash policy. Unlike previous methods, INPO bypasses the need for estimating the expected win rate for individual responses, which typically incurs high computational or annotation costs. Instead, we introduce a new loss objective that is directly minimized over a preference dataset. We provide theoretical analysis for our approach and demonstrate its effectiveness through experiments on various representative benchmarks. With an LLaMA-3-8B-based SFT model, INPO achieves a 41.5% length-controlled win rate on AlpacaEval 2.0 and a 38.3% win rate on Arena-Hard, showing substantial improvement over the state-of-the-art iterative algorithm [Dong et al., 2024] under the BT model assumption. Additionally, our ablation study highlights the benefits of incorporating KL regularization for response length control.

Recent reinforcement learning approaches, such as outcome-supervised GRPO, have advanced Chain-of-Thought reasoning in large language models (LLMs), yet their adaptation to multimodal LLMs (MLLMs) is unexplored. To address the lack of rigorous evaluation for MLLM post-training methods, we introduce SEED-Bench-R1, a benchmark with complex real-world videos requiring balanced perception and reasoning. It offers a large training set and evaluates generalization across three escalating challenges: in-distribution, cross-environment, and cross-environment-task scenarios. Using SEED-Bench-R1, we find that standard GRPO, while improving answer accuracy, often reduces logical coherence between reasoning steps and answers, with only a 57.9% consistency rate. This stems from reward signals focusing solely on final answers, encouraging shortcuts, and strict KL penalties limiting exploration.To address this, we propose GRPO-CARE, a consistency-aware RL framework optimizing both answer correctness and reasoning coherence without explicit supervision. GRPO-CARE introduces a two-tiered reward: (1) a base reward for answer correctness, and (2) an adaptive consistency bonus, computed by comparing the model's reasoning-to-answer likelihood (via a slowly-evolving reference model) against group peers.This dual mechanism amplifies rewards for reasoning paths that are both correct and logically consistent. Replacing KL penalties with this adaptive bonus, GRPO-CARE outperforms standard GRPO on SEED-Bench-R1, achieving a 6.7% performance gain on the hardest evaluation level and a 24.5% improvement in consistency. It also shows strong transferability, improving model performance across diverse video understanding benchmarks. Our work contributes a systematically designed benchmark and a generalizable post-training framework, advancing the development of more interpretable and robust MLLMs.

Model-based reinforcement learning (RL) offers a solution to the data inefficiency that plagues most model-free RL algorithms. However, learning a robust world model often requires complex and deep architectures, which are computationally expensive and challenging to train. Within the world model, sequence models play a critical role in accurate predictions, and various architectures have been explored, each with its own challenges. Currently, recurrent neural network (RNN)-based world models struggle with vanishing gradients and capturing long-term dependencies. Transformers, on the other hand, suffer from the quadratic memory and computational complexity of self-attention mechanisms, scaling as O(n^2), where n is the sequence length. To address these challenges, we propose a state space model (SSM)-based world model, Drama, specifically leveraging Mamba, that achieves O(n) memory and computational complexity while effectively capturing long-term dependencies and enabling efficient training with longer sequences. We also introduce a novel sampling method to mitigate the suboptimality caused by an incorrect world model in the early training stages. Combining these techniques, Drama achieves a normalised score on the Atari100k benchmark that is competitive with other state-of-the-art (SOTA) model-based RL algorithms, using only a 7 million-parameter world model. Drama is accessible and trainable on off-the-shelf hardware, such as a standard laptop. Our code is available at https://github.com/realwenlongwang/Drama.git.

Designing effective reasoning-capable LLMs typically requires training using Reinforcement Learning with Verifiable Rewards (RLVR) or distillation with carefully curated Long Chain of Thoughts (CoT), both of which depend heavily on extensive training data. This creates a major challenge when the amount of quality training data is scarce. We propose a sample-efficient, two-stage training strategy to develop reasoning LLMs under limited supervision. In the first stage, we "warm up" the model by distilling Long CoTs from a toy domain, namely, Knights \& Knaves (K\&K) logic puzzles to acquire general reasoning skills. In the second stage, we apply RLVR to the warmed-up model using a limited set of target-domain examples. Our experiments demonstrate that this two-phase approach offers several benefits: (i) the warmup phase alone facilitates generalized reasoning, leading to performance improvements across a range of tasks, including MATH, HumanEval^{+}, and MMLU-Pro. (ii) When both the base model and the warmed-up model are RLVR trained on the same small dataset (leq100 examples), the warmed-up model consistently outperforms the base model; (iii) Warming up before RLVR training allows a model to maintain cross-domain generalizability even after training on a specific domain; (iv) Introducing warmup in the pipeline improves not only accuracy but also overall sample efficiency during RLVR training. The results in this paper highlight the promise of warmup for building robust reasoning LLMs in data-scarce environments.

Risk-sensitive reinforcement learning (RL) aims to optimize policies that balance the expected reward and risk. In this paper, we present a novel risk-sensitive RL framework that employs an Iterated Conditional Value-at-Risk (CVaR) objective under both linear and general function approximations, enriched by human feedback. These new formulations provide a principled way to guarantee safety in each decision making step throughout the control process. Moreover, integrating human feedback into risk-sensitive RL framework bridges the gap between algorithmic decision-making and human participation, allowing us to also guarantee safety for human-in-the-loop systems. We propose provably sample-efficient algorithms for this Iterated CVaR RL and provide rigorous theoretical analysis. Furthermore, we establish a matching lower bound to corroborate the optimality of our algorithms in a linear context.

Reinforcement learning (RL) problems can be challenging without well-shaped rewards. Prior work on provably efficient RL methods generally proposes to address this issue with dedicated exploration strategies. However, another way to tackle this challenge is to reformulate it as a multi-task RL problem, where the task space contains not only the challenging task of interest but also easier tasks that implicitly function as a curriculum. Such a reformulation opens up the possibility of running existing multi-task RL methods as a more efficient alternative to solving a single challenging task from scratch. In this work, we provide a theoretical framework that reformulates a single-task RL problem as a multi-task RL problem defined by a curriculum. Under mild regularity conditions on the curriculum, we show that sequentially solving each task in the multi-task RL problem is more computationally efficient than solving the original single-task problem, without any explicit exploration bonuses or other exploration strategies. We also show that our theoretical insights can be translated into an effective practical learning algorithm that can accelerate curriculum learning on simulated robotic tasks.

Reinforcement Learning with Verifiable Rewards (RLVR) has emerged as a powerful paradigm for enhancing the reasoning capabilities of LLMs. Existing research has predominantly concentrated on isolated reasoning domains such as mathematical problem-solving, coding tasks, or logical reasoning. However, real world reasoning scenarios inherently demand an integrated application of multiple cognitive skills. Despite this, the interplay among these reasoning skills under reinforcement learning remains poorly understood. To bridge this gap, we present a systematic investigation of multi-domain reasoning within the RLVR framework, explicitly focusing on three primary domains: mathematical reasoning, code generation, and logical puzzle solving. We conduct a comprehensive study comprising four key components: (1) Leveraging the GRPO algorithm and the Qwen-2.5-7B model family, our study thoroughly evaluates the models' in-domain improvements and cross-domain generalization capabilities when trained on single-domain datasets. (2) Additionally, we examine the intricate interactions including mutual enhancements and conflicts that emerge during combined cross-domain training. (3) To further understand the influence of SFT on RL, we also analyze and compare performance differences between base and instruct models under identical RL configurations. (4) Furthermore, we delve into critical RL training details, systematically exploring the impacts of curriculum learning strategies, variations in reward design, and language-specific factors. Through extensive experiments, our results offer significant insights into the dynamics governing domain interactions, revealing key factors influencing both specialized and generalizable reasoning performance. These findings provide valuable guidance for optimizing RL methodologies to foster comprehensive, multi-domain reasoning capabilities in LLMs.

Recent advancements in Large Language Models (LLMs) have garnered wide attention and led to successful products such as ChatGPT and GPT-4. Their proficiency in adhering to instructions and delivering harmless, helpful, and honest (3H) responses can largely be attributed to the technique of Reinforcement Learning from Human Feedback (RLHF). In this paper, we aim to link the research in conventional RL to RL techniques used in LLM research. Demystify this technique by discussing why, when, and how RL excels. Furthermore, we explore potential future avenues that could either benefit from or contribute to RLHF research. Highlighted Takeaways: 1. RLHF is Online Inverse RL with Offline Demonstration Data. 2. RLHF > SFT because Imitation Learning (and Inverse RL) > Behavior Cloning (BC) by alleviating the problem of compounding error. 3. The RM step in RLHF generates a proxy of the expensive human feedback, such an insight can be generalized to other LLM tasks such as prompting evaluation and optimization where feedback is also expensive. 4. The policy learning in RLHF is more challenging than conventional problems studied in IRL due to their high action dimensionality and feedback sparsity. 5. The main superiority of PPO over off-policy value-based methods is its stability gained from (almost) on-policy data and conservative policy updates.

We propose Reinforcement Learning with Explicit Human Values (RLEV), a method that aligns Large Language Model (LLM) optimization directly with quantifiable human value signals. While Reinforcement Learning with Verifiable Rewards (RLVR) effectively trains models in objective domains using binary correctness rewards, it overlooks that not all tasks are equally significant. RLEV extends this framework by incorporating human-defined value signals directly into the reward function. Using exam-style data with explicit ground-truth value labels, RLEV consistently outperforms correctness-only baselines across multiple RL algorithms and model scales. Crucially, RLEV policies not only improve value-weighted accuracy but also learn a value-sensitive termination policy: concise for low-value prompts, thorough for high-value ones. We demonstrate this behavior stems from value-weighted gradient amplification on end-of-sequence tokens. Ablation studies confirm the gain is causally linked to value alignment. RLEV remains robust under noisy value signals, such as difficulty-based labels, demonstrating that optimizing for an explicit utility function offers a practical path to aligning LLMs with human priorities.

Prevalent reinforcement learning~(RL) methods for fine-tuning LLM reasoners, such as GRPO or Leave-one-out PPO, abandon the learned value function in favor of empirically estimated returns. This hinders test-time compute scaling that relies on using the value-function for verification. In this work, we propose RL^V that augments any ``value-free'' RL method by jointly training the LLM as both a reasoner and a generative verifier using RL-generated data, adding verification capabilities without significant overhead. Empirically, RL^V boosts MATH accuracy by over 20\% with parallel sampling and enables 8-32times efficient test-time compute scaling compared to the base RL method. RL^V also exhibits strong generalization capabilities for both easy-to-hard and out-of-domain tasks. Furthermore, RL^V achieves 1.2-1.6times higher performance when jointly scaling parallel and sequential test-time compute with a long reasoning R1 model.

Reinforcement learning with verifiable rewards (RLVR) has emerged as a promising paradigm for enhancing the reasoning capabilities of large language models (LLMs). In this context, models explore reasoning trajectories and exploit rollouts with correct answers as positive signals for policy optimization. However, these rollouts might involve flawed patterns such as answer-guessing and jump-in-reasoning. Such flawed-positive rollouts are rewarded identically to fully correct ones, causing policy models to internalize these unreliable reasoning patterns. In this work, we first conduct a systematic study of flawed-positive rollouts in RL and find that they enable rapid capability gains during the early optimization stage, while constraining reasoning capability later by reinforcing unreliable patterns. Building on these insights, we propose Flawed-Aware Policy Optimization (FAPO), which presents a parameter-free reward penalty for flawed-positive rollouts, enabling the policy to leverage them as useful shortcuts in the warm-up stage, securing stable early gains, while gradually shifting optimization toward reliable reasoning in the later refinement stage. To accurately and comprehensively detect flawed-positive rollouts, we introduce a generative reward model (GenRM) with a process-level reward that precisely localizes reasoning errors. Experiments show that FAPO is effective in broad domains, improving outcome correctness, process reliability, and training stability without increasing the token budget.

We investigate reinforcement learning (RL) for privileged planning in autonomous driving. State-of-the-art approaches for this task are rule-based, but these methods do not scale to the long tail. RL, on the other hand, is scalable and does not suffer from compounding errors like imitation learning. Contemporary RL approaches for driving use complex shaped rewards that sum multiple individual rewards, \eg~progress, position, or orientation rewards. We show that PPO fails to optimize a popular version of these rewards when the mini-batch size is increased, which limits the scalability of these approaches. Instead, we propose a new reward design based primarily on optimizing a single intuitive reward term: route completion. Infractions are penalized by terminating the episode or multiplicatively reducing route completion. We find that PPO scales well with higher mini-batch sizes when trained with our simple reward, even improving performance. Training with large mini-batch sizes enables efficient scaling via distributed data parallelism. We scale PPO to 300M samples in CARLA and 500M samples in nuPlan with a single 8-GPU node. The resulting model achieves 64 DS on the CARLA longest6 v2 benchmark, outperforming other RL methods with more complex rewards by a large margin. Requiring only minimal adaptations from its use in CARLA, the same method is the best learning-based approach on nuPlan. It scores 91.3 in non-reactive and 90.6 in reactive traffic on the Val14 benchmark while being an order of magnitude faster than prior work.

Most offline reinforcement learning (RL) algorithms return a target policy maximizing a trade-off between (1) the expected performance gain over the behavior policy that collected the dataset, and (2) the risk stemming from the out-of-distribution-ness of the induced state-action occupancy. It follows that the performance of the target policy is strongly related to the performance of the behavior policy and, thus, the trajectory return distribution of the dataset. We show that in mixed datasets consisting of mostly low-return trajectories and minor high-return trajectories, state-of-the-art offline RL algorithms are overly restrained by low-return trajectories and fail to exploit high-performing trajectories to the fullest. To overcome this issue, we show that, in deterministic MDPs with stochastic initial states, the dataset sampling can be re-weighted to induce an artificial dataset whose behavior policy has a higher return. This re-weighted sampling strategy may be combined with any offline RL algorithm. We further analyze that the opportunity for performance improvement over the behavior policy correlates with the positive-sided variance of the returns of the trajectories in the dataset. We empirically show that while CQL, IQL, and TD3+BC achieve only a part of this potential policy improvement, these same algorithms combined with our reweighted sampling strategy fully exploit the dataset. Furthermore, we empirically demonstrate that, despite its theoretical limitation, the approach may still be efficient in stochastic environments. The code is available at https://github.com/Improbable-AI/harness-offline-rl.

Modern large reasoning models demonstrate impressive problem-solving capabilities by employing sophisticated reasoning strategies. However, they often struggle to balance efficiency and effectiveness, frequently generating unnecessarily lengthy reasoning chains for simple problems. In this work, we propose AdaCtrl, a novel framework to support both difficulty-aware adaptive reasoning budget allocation and explicit user control over reasoning depth. AdaCtrl dynamically adjusts its reasoning length based on self-assessed problem difficulty, while also allowing users to manually control the budget to prioritize either efficiency or effectiveness. This is achieved through a two-stage training pipeline: an initial cold-start fine-tuning phase to instill the ability to self-aware difficulty and adjust reasoning budget, followed by a difficulty-aware reinforcement learning (RL) stage that refines the model's adaptive reasoning strategies and calibrates its difficulty assessments based on its evolving capabilities during online training. To enable intuitive user interaction, we design explicit length-triggered tags that function as a natural interface for budget control. Empirical results show that AdaCtrl adapts reasoning length based on estimated difficulty, compared to the standard training baseline that also incorporates fine-tuning and RL, it yields performance improvements and simultaneously reduces response length by 10.06% and 12.14% on the more challenging AIME2024 and AIME2025 datasets, which require elaborate reasoning, and by 62.05% and 91.04% on the MATH500 and GSM8K datasets, where more concise responses are sufficient. Furthermore, AdaCtrl enables precise user control over the reasoning budget, allowing for tailored responses to meet specific needs.

Reinforcement learning (RL) has significantly advanced code generation for large language models (LLMs). However, current paradigms rely on outcome-based rewards from test cases, neglecting the quality of the intermediate reasoning process. While supervising the reasoning process directly is a promising direction, it is highly susceptible to reward hacking, where the policy model learns to exploit the reasoning reward signal without improving final outcomes. To address this, we introduce a unified framework that can effectively incorporate the quality of the reasoning process during RL. First, to enable reasoning evaluation, we develop LCB-RB, a benchmark comprising preference pairs of superior and inferior reasoning processes. Second, to accurately score reasoning quality, we introduce an Optimized-Degraded based (OD-based) method for reward model training. This method generates high-quality preference pairs by systematically optimizing and degrading initial reasoning paths along curated dimensions of reasoning quality, such as factual accuracy, logical rigor, and coherence. A 7B parameter reward model with this method achieves state-of-the-art (SOTA) performance on LCB-RB and generalizes well to other benchmarks. Finally, we introduce Posterior-GRPO (P-GRPO), a novel RL method that conditions process-based rewards on task success. By selectively applying rewards to the reasoning processes of only successful outcomes, P-GRPO effectively mitigates reward hacking and aligns the model's internal reasoning with final code correctness. A 7B parameter model with P-GRPO achieves superior performance across diverse code generation tasks, outperforming outcome-only baselines by 4.5%, achieving comparable performance to GPT-4-Turbo. We further demonstrate the generalizability of our approach by extending it to mathematical tasks. Our models, dataset, and code are publicly available.

Reinforcement learning (RL) is rapidly reaching and surpassing human-level control capabilities. However, state-of-the-art RL algorithms often require timesteps and reaction times significantly faster than human capabilities, which is impractical in real-world settings and typically necessitates specialized hardware. Such speeds are difficult to achieve in the real world and often requires specialized hardware. We introduce Sequence Reinforcement Learning (SRL), an RL algorithm designed to produce a sequence of actions for a given input state, enabling effective control at lower decision frequencies. SRL addresses the challenges of learning action sequences by employing both a model and an actor-critic architecture operating at different temporal scales. We propose a "temporal recall" mechanism, where the critic uses the model to estimate intermediate states between primitive actions, providing a learning signal for each individual action within the sequence. Once training is complete, the actor can generate action sequences independently of the model, achieving model-free control at a slower frequency. We evaluate SRL on a suite of continuous control tasks, demonstrating that it achieves performance comparable to state-of-the-art algorithms while significantly reducing actor sample complexity. To better assess performance across varying decision frequencies, we introduce the Frequency-Averaged Score (FAS) metric. Our results show that SRL significantly outperforms traditional RL algorithms in terms of FAS, making it particularly suitable for applications requiring variable decision frequencies. Additionally, we compare SRL with model-based online planning, showing that SRL achieves superior FAS while leveraging the same model during training that online planners use for planning.

Recent advances in Large Language Models (LLMs) have underscored the potential of Reinforcement Learning (RL) to facilitate the emergence of reasoning capabilities. Despite the encouraging results, a fundamental dilemma persists as RL improvement relies on learning from high-quality samples, yet the exploration for such samples remains bounded by the inherent limitations of LLMs. This, in effect, creates an undesirable cycle in which what cannot be explored cannot be learned. In this work, we propose Rubric-Scaffolded Reinforcement Learning (RuscaRL), a novel instructional scaffolding framework designed to break the exploration bottleneck for general LLM reasoning. Specifically, RuscaRL introduces checklist-style rubrics as (1) explicit scaffolding for exploration during rollout generation, where different rubrics are provided as external guidance within task instructions to steer diverse high-quality responses. This guidance is gradually decayed over time, encouraging the model to internalize the underlying reasoning patterns; (2) verifiable rewards for exploitation during model training, where we can obtain robust LLM-as-a-Judge scores using rubrics as references, enabling effective RL on general reasoning tasks. Extensive experiments demonstrate the superiority of the proposed RuscaRL across various benchmarks, effectively expanding reasoning boundaries under the best-of-N evaluation. Notably, RuscaRL significantly boosts Qwen-2.5-7B-Instruct from 23.6 to 50.3 on HealthBench-500, surpassing GPT-4.1. Furthermore, our fine-tuned variant on Qwen3-30B-A3B-Instruct achieves 61.1 on HealthBench-500, outperforming leading LLMs including OpenAI-o3.

Natural agents can effectively learn from multiple data sources that differ in size, quality, and types of measurements. We study this heterogeneity in the context of offline reinforcement learning (RL) by introducing a new, practically motivated semi-supervised setting. Here, an agent has access to two sets of trajectories: labelled trajectories containing state, action and reward triplets at every timestep, along with unlabelled trajectories that contain only state and reward information. For this setting, we develop and study a simple meta-algorithmic pipeline that learns an inverse dynamics model on the labelled data to obtain proxy-labels for the unlabelled data, followed by the use of any offline RL algorithm on the true and proxy-labelled trajectories. Empirically, we find this simple pipeline to be highly successful -- on several D4RL benchmarks~fu2020d4rl, certain offline RL algorithms can match the performance of variants trained on a fully labelled dataset even when we label only 10\% of trajectories which are highly suboptimal. To strengthen our understanding, we perform a large-scale controlled empirical study investigating the interplay of data-centric properties of the labelled and unlabelled datasets, with algorithmic design choices (e.g., choice of inverse dynamics, offline RL algorithm) to identify general trends and best practices for training RL agents on semi-supervised offline datasets.

Reinforcement learning with verifiable rewards (RLVR) is a promising approach for training language models (LMs) on reasoning tasks that elicit emergent long chains of thought (CoTs). Unlike supervised learning, it updates the model using both correct and incorrect samples via policy gradients. To better understand its mechanism, we decompose the learning signal into reinforcing correct responses and penalizing incorrect ones, referred to as Positive and Negative Sample Reinforcement (PSR and NSR), respectively. We train Qwen2.5-Math-7B and Qwen3-4B on a mathematical reasoning dataset and uncover a surprising result: training with only negative samples -- without reinforcing correct responses -- can be highly effective: it consistently improves performance over the base model across the entire Pass@k spectrum (k up to 256), often matching or surpassing PPO and GRPO. In contrast, reinforcing only correct responses improves Pass@1 but degrades performance at higher k, due to reduced diversity. These inference-scaling trends highlight that solely penalizing incorrect responses may contribute more to performance than previously recognized. Through gradient analysis, we show that NSR works by suppressing incorrect generations and redistributing probability mass toward other plausible candidates, guided by the model's prior beliefs. It refines the model's existing knowledge rather than introducing entirely new behaviors. Building on this insight, we propose a simple variant of the RL objective that upweights NSR, and show that it consistently improves overall Pass@k performance on MATH, AIME 2025, and AMC23. Our code is available at https://github.com/TianHongZXY/RLVR-Decomposed.

Recent advances in large language model (LLM) reasoning have shown that sophisticated behaviors such as planning and self-reflection can emerge through reinforcement learning (RL). However, despite these successes, RL in its current form remains insufficient to induce capabilities that exceed the limitations of the base model, as it is primarily optimized based on existing knowledge of the model rather than facilitating the acquisition of new information. To address this limitation, we employ supervised fine-tuning (SFT) to learn what RL cannot, which enables the incorporation of new knowledge and reasoning patterns by leveraging high-quality demonstration data. We analyze the training dynamics of RL and SFT for LLM reasoning and find that RL excels at maintaining and improving performance on questions within the model's original capabilities, while SFT is more effective at enabling progress on questions beyond the current scope of the model. Motivated by the complementary strengths of RL and SFT, we introduce a novel training approach, ReLIFT (Reinforcement Learning Interleaved with Online Fine-Tuning). In ReLIFT, the model is primarily trained using RL, but when it encounters challenging questions, high-quality solutions are collected for fine-tuning, and the training process alternates between RL and fine-tuning to enhance the model's reasoning abilities. ReLIFT achieves an average improvement of over +5.2 points across five competition-level benchmarks and one out-of-distribution benchmark compared to other zero-RL models. Furthermore, we demonstrate that ReLIFT outperforms both RL and SFT while using only 13\% of the detailed demonstration data, highlighting its scalability. These results provide compelling evidence that ReLIFT overcomes the fundamental limitations of RL and underscores the significant potential.

Reinforcement learning from human feedback (RLHF) has become an important technical and storytelling tool to deploy the latest machine learning systems. In this book, we hope to give a gentle introduction to the core methods for people with some level of quantitative background. The book starts with the origins of RLHF -- both in recent literature and in a convergence of disparate fields of science in economics, philosophy, and optimal control. We then set the stage with definitions, problem formulation, data collection, and other common math used in the literature. The core of the book details every optimization stage in using RLHF, from starting with instruction tuning to training a reward model and finally all of rejection sampling, reinforcement learning, and direct alignment algorithms. The book concludes with advanced topics -- understudied research questions in synthetic data and evaluation -- and open questions for the field.

Offline reinforcement learning (RL) aims to learn from historical data without requiring (costly) access to the environment. To facilitate offline RL research, we previously introduced NeoRL, which highlighted that datasets from real-world tasks are often conservative and limited. With years of experience applying offline RL to various domains, we have identified additional real-world challenges. These include extremely conservative data distributions produced by deployed control systems, delayed action effects caused by high-latency transitions, external factors arising from the uncontrollable variance of transitions, and global safety constraints that are difficult to evaluate during the decision-making process. These challenges are underrepresented in previous benchmarks but frequently occur in real-world tasks. To address this, we constructed the extended Near Real-World Offline RL Benchmark (NeoRL-2), which consists of 7 datasets from 7 simulated tasks along with their corresponding evaluation simulators. Benchmarking results from state-of-the-art offline RL approaches demonstrate that current methods often struggle to outperform the data-collection behavior policy, highlighting the need for more effective methods. We hope NeoRL-2 will accelerate the development of reinforcement learning algorithms for real-world applications. The benchmark project page is available at https://github.com/polixir/NeoRL2.

Current approaches for training Process Reward Models (PRMs) often involve breaking down responses into multiple reasoning steps using rule-based techniques, such as using predefined placeholder tokens or setting the reasoning step's length into a fixed size. These approaches overlook the fact that specific words do not typically mark true decision points in a text. To address this, we propose AdaptiveStep, a method that divides reasoning steps based on the model's confidence in predicting the next word. This division method provides more decision-making information at each step, enhancing downstream tasks, such as reward model learning. Moreover, our method does not require manual annotation. We demonstrate its effectiveness through experiments with AdaptiveStep-trained PRMs in mathematical reasoning and code generation tasks. Experimental results indicate that the outcome PRM achieves state-of-the-art Best-of-N performance, surpassing greedy search strategy with token-level value-guided decoding, while also reducing construction costs by over 30% compared to existing open-source PRMs. In addition, we provide a thorough analysis and case study on the PRM's performance, transferability, and generalization capabilities.

Large language models (LLMs) inevitably make mistakes when performing step-by-step mathematical reasoning. Process Reward Models (PRMs) have emerged as a promising solution by evaluating each reasoning step. However, existing PRMs typically output evaluation scores directly, limiting both learning efficiency and evaluation accuracy, which is further exacerbated by the scarcity of annotated data. To address these issues, we propose Reasoning-Driven Process Reward Modeling (R-PRM). First, we leverage stronger LLMs to generate seed data from limited annotations, effectively bootstrapping our model's reasoning capabilities and enabling comprehensive step-by-step evaluation. Second, we further enhance performance through preference optimization, without requiring additional annotated data. Third, we introduce inference-time scaling to fully harness the model's reasoning potential. Extensive experiments demonstrate R-PRM's effectiveness: on ProcessBench and PRMBench, it surpasses strong baselines by 11.9 and 8.5 points in F1 scores, respectively. When applied to guide mathematical reasoning, R-PRM achieves consistent accuracy improvements of over 8.5 points across six challenging datasets. Further analysis reveals that R-PRM exhibits more comprehensive evaluation and stronger generalization capabilities, thereby highlighting its significant potential.

Reinforcement learning (RL) has shown impressive results in sequential decision-making tasks. Meanwhile, Large Language Models (LLMs) and Vision-Language Models (VLMs) have emerged, exhibiting impressive capabilities in multimodal understanding and reasoning. These advances have led to a surge of research integrating LLMs and VLMs into RL. In this survey, we review representative works in which LLMs and VLMs are used to overcome key challenges in RL, such as lack of prior knowledge, long-horizon planning, and reward design. We present a taxonomy that categorizes these LLM/VLM-assisted RL approaches into three roles: agent, planner, and reward. We conclude by exploring open problems, including grounding, bias mitigation, improved representations, and action advice. By consolidating existing research and identifying future directions, this survey establishes a framework for integrating LLMs and VLMs into RL, advancing approaches that unify natural language and visual understanding with sequential decision-making.

Reinforcement fine-tuning (RFT) has emerged as a powerful post-training technique to incentivize the reasoning ability of large language models (LLMs). However, LLMs can respond very inconsistently to RFT: some show substantial performance gains, while others plateau or even degrade. To understand this divergence, we analyze the per-step influence of the RL objective and identify two key conditions for effective post-training: (1) RL-informative rollout accuracy, and (2) strong data co-influence, which quantifies how much the training data affects performance on other samples. Guided by these insights, we propose behavior injection, a task-agnostic data-augmentation scheme applied prior to RL. Behavior injection enriches the supervised finetuning (SFT) data by seeding exploratory and exploitative behaviors, effectively making the model more RL-ready. We evaluate our method across two reasoning benchmarks with multiple base models. The results demonstrate that our theoretically motivated augmentation can significantly increases the performance gain from RFT over the pre-RL model.

Large language models (LLMs) excel at reasoning, yet post-training remains critical for aligning their behavior with task goals. Existing reinforcement learning (RL) methods often depend on costly human annotations or external reward models. We propose Reinforcement Learning via Self-Confidence (RLSC), which uses the model's own confidence as reward signals-eliminating the need for labels, preference models, or reward engineering. Applied to Qwen2.5-Math-7B with only 16 samples per question and 10 or 20 training steps, RLSC improves accuracy by +13.4% on AIME2024, +21.2% on MATH500, +21.7% on Minerva Math, +20.8% on Olympiadbench, and +9.7% on AMC23. RLSC provides a simple, scalable post-training method for inference models, requiring only a small number of samples and unlabelled supervision.

Large language models (LLMs) provide excellent text-generation capabilities, but standard prompting and generation methods generally do not lead to intentional or goal-directed agents and might necessitate considerable prompt tuning. This becomes particularly apparent in multi-turn conversations: even the best current LLMs rarely ask clarifying questions, engage in explicit information gathering, or take actions now that lead to better decisions after multiple turns. Reinforcement learning has the potential to leverage the powerful modeling capabilities of LLMs, as well as their internal representation of textual interactions, to create capable goal-directed language agents. This can enable intentional and temporally extended interactions, such as with humans, through coordinated persuasion and carefully crafted questions, or in goal-directed play through text games to bring about desired final outcomes. However, enabling this requires the community to develop stable and reliable reinforcement learning algorithms that can effectively train LLMs. Developing such algorithms requires tasks that can gauge progress on algorithm design, provide accessible and reproducible evaluations for multi-turn interactions, and cover a range of task properties and challenges in improving reinforcement learning algorithms. Our paper introduces the LMRL-Gym benchmark for evaluating multi-turn RL for LLMs, together with an open-source research framework containing a basic toolkit for getting started on multi-turn RL with offline value-based and policy-based RL methods. Our benchmark consists of 8 different language tasks, which require multiple rounds of language interaction and cover a range of tasks in open-ended dialogue and text games.

Recent works demonstrate that using reinforcement learning (RL) with quality rewards can enhance the quality of generated images in text-to-image (T2I) generation. However, a simple aggregation of multiple rewards may cause over-optimization in certain metrics and degradation in others, and it is challenging to manually find the optimal weights. An effective strategy to jointly optimize multiple rewards in RL for T2I generation is highly desirable. This paper introduces Parrot, a novel multi-reward RL framework for T2I generation. Through the use of the batch-wise Pareto optimal selection, Parrot automatically identifies the optimal trade-off among different rewards during the RL optimization of the T2I generation. Additionally, Parrot employs a joint optimization approach for the T2I model and the prompt expansion network, facilitating the generation of quality-aware text prompts, thus further enhancing the final image quality. To counteract the potential catastrophic forgetting of the original user prompt due to prompt expansion, we introduce original prompt centered guidance at inference time, ensuring that the generated image remains faithful to the user input. Extensive experiments and a user study demonstrate that Parrot outperforms several baseline methods across various quality criteria, including aesthetics, human preference, image sentiment, and text-image alignment.

Existing agents for solving tasks such as ML engineering rely on prompting powerful language models. As a result, these agents do not improve with more experience. In this paper, we show that agents backed by weaker models that improve via reinforcement learning (RL) can outperform agents backed by much larger, but static models. We identify two major challenges with RL in this setting. First, actions can take a variable amount of time (e.g., executing code for different solutions), which leads to asynchronous policy gradient updates that favor faster but suboptimal solutions. To tackle variable-duration actions, we propose duration-aware gradient updates in a distributed asynchronous RL framework to amplify high-cost but high-reward actions. Second, using only test split performance as a reward provides limited feedback. A program that is nearly correct is treated the same as one that fails entirely. To address this, we propose environment instrumentation to offer partial credit, distinguishing almost-correct programs from those that fail early (e.g., during data loading). Environment instrumentation uses a separate static language model to insert print statement to an existing program to log the agent's experimental progress, from which partial credit can be extracted as reward signals for learning. Our experimental results on MLEBench suggest that performing gradient updates on a much smaller model (Qwen2.5-3B) trained with RL outperforms prompting a much larger model (Claude-3.5-Sonnet) with agent scaffolds, by an average of 22% across 12 Kaggle tasks.

The past few years have seen rapid progress in combining reinforcement learning (RL) with deep learning. Various breakthroughs ranging from games to robotics have spurred the interest in designing sophisticated RL algorithms and systems. However, the prevailing workflow in RL is to learn tabula rasa, which may incur computational inefficiency. This precludes continuous deployment of RL algorithms and potentially excludes researchers without large-scale computing resources. In many other areas of machine learning, the pretraining paradigm has shown to be effective in acquiring transferable knowledge, which can be utilized for a variety of downstream tasks. Recently, we saw a surge of interest in Pretraining for Deep RL with promising results. However, much of the research has been based on different experimental settings. Due to the nature of RL, pretraining in this field is faced with unique challenges and hence requires new design principles. In this survey, we seek to systematically review existing works in pretraining for deep reinforcement learning, provide a taxonomy of these methods, discuss each sub-field, and bring attention to open problems and future directions.

Process Reward Models (PRMs) aim to improve multi-step reasoning in Large Language Models (LLMs) by supervising intermediate steps and identifying errors. However, building effective PRMs remains challenging due to the lack of scalable, high-quality annotations. Existing approaches rely on costly human labeling, LLM-based self-evaluation that is prone to hallucination, or Monte Carlo (MC) estimation, which infers step quality solely from rollout outcomes and often introduces noisy, misaligned supervision due to credit misattribution. These issues result in three core limitations: noisy rewards, low factual fidelity, and misalignment with step-level reasoning objectives. To address these challenges, we introduce GroundedPRM, a tree-guided and fidelity-aware framework for automatic process supervision. To reduce reward noise and enable fine-grained credit assignment, we construct structured reasoning paths via Monte Carlo Tree Search (MCTS). To eliminate hallucinated supervision, we validate each intermediate step using an external tool, providing execution-grounded correctness signals. To combine both step-level validation and global outcome assessment, we design a hybrid reward aggregation mechanism that fuses tool-based verification with MCTS-derived feedback. Finally, we format the reward signal into a rationale-enhanced, generative structure to promote interpretability and compatibility with instruction-tuned LLMs. GroundedPRM is trained on only 40K automatically labeled samples, amounting to just 10% of the data used by the best-performing PRM trained with auto-labeled supervision. Nevertheless, it achieves up to a 26% relative improvement in average performance on ProcessBench. When used for reward-guided greedy search, GroundedPRM outperforms even PRMs trained with human-labeled supervision, offering a scalable and verifiable path toward high-quality process-level reasoning.

Recent advances in reasoning-centric language models have highlighted reinforcement learning (RL) as a promising method for aligning models with verifiable rewards. However, it remains contentious whether RL truly expands a model's reasoning capabilities or merely amplifies high-reward outputs already latent in the base model's distribution, and whether continually scaling up RL compute reliably leads to improved reasoning performance. In this work, we challenge prevailing assumptions by demonstrating that prolonged RL (ProRL) training can uncover novel reasoning strategies that are inaccessible to base models, even under extensive sampling. We introduce ProRL, a novel training methodology that incorporates KL divergence control, reference policy resetting, and a diverse suite of tasks. Our empirical analysis reveals that RL-trained models consistently outperform base models across a wide range of pass@k evaluations, including scenarios where base models fail entirely regardless of the number of attempts. We further show that reasoning boundary improvements correlates strongly with task competence of base model and training duration, suggesting that RL can explore and populate new regions of solution space over time. These findings offer new insights into the conditions under which RL meaningfully expands reasoning boundaries in language models and establish a foundation for future work on long-horizon RL for reasoning. We release model weights to support further research: https://huggingface.co/nvidia/Nemotron-Research-Reasoning-Qwen-1.5B

Recent advancements in large language models (LLMs) have witnessed a surge in the development of advanced reasoning paradigms, which are now being integrated into multimodal large language models (MLLMs). However, existing approaches often fall short: methods solely employing reinforcement learning (RL) can struggle with sample inefficiency and activating entirely absent reasoning capabilities, while conventional pipelines that initiate with a cold-start supervised fine-tuning (SFT) phase before RL may restrict the model's exploratory capacity and face suboptimal convergence. In this work, we introduce Metis-RISE (RL Incentivizes and SFT Enhances) for multimodal reasoning model learning. Unlike conventional approaches, Metis-RISE distinctively omits an initial SFT stage, beginning instead with an RL phase (e.g., using a Group Relative Policy Optimization variant) to incentivize and activate the model's latent reasoning capacity. Subsequently, the targeted SFT stage addresses two key challenges identified during RL: (1) inefficient trajectory sampling for tasks where the model possesses but inconsistently applies correct reasoning, which we tackle using self-distilled reasoning trajectories from the RL model itself; and (2) fundamental capability absence, which we address by injecting expert-augmented knowledge for prompts where the model entirely fails. This strategic application of RL for incentivization followed by SFT for enhancement forms the core of Metis-RISE, leading to two versions of our MLLMs (7B and 72B parameters). Evaluations on the OpenCompass Multimodal Reasoning Leaderboard demonstrate that both models achieve state-of-the-art performance among similar-sized models, with the 72B version ranking fourth overall.

The rapid emergence of diverse large language models (LLMs) has spurred the development of LLM routers that assign user queries to the most suitable model. However, existing LLM routers typically perform a single-round, one-to-one mapping (i.e., assigning each query to a single model in isolation), which limits their capability to tackle complex tasks that demand the complementary strengths of multiple LLMs. In this paper, we present Router-R1, a reinforcement learning (RL)-based framework that formulates multi-LLM routing and aggregation as a sequential decision process. Router-R1 instantiates the router itself as a capable LLM, leveraging its reasoning ability to interleave "think" actions (internal deliberation) with "route" actions (dynamic model invocation), and integrates each response into its evolving context. To guide learning, we employ a lightweight rule-based reward comprising format rewards, final outcome rewards, and a novel cost reward for performance and cost trade-off optimization, opening a pathway toward optimizing performance-cost tradeoffs via RL. Router-R1 also conditions only on simple model descriptors such as pricing, latency, and example performance, enabling strong generalization to unseen model selection. Experiments on seven general and multi-hop QA benchmarks show that Router-R1 outperforms over several strong baselines, achieving superior performance while maintaining robust generalization and cost management.Code is available at https://github.com/ulab-uiuc/Router-R1.

Reinforcement Learning (RL) has become a powerful tool for enhancing the reasoning abilities of large language models (LLMs) by optimizing their policies with reward signals. Yet, RL's success relies on the reliability of rewards, which are provided by verifiers. In this paper, we expose and analyze a widespread problem--false negatives--where verifiers wrongly reject correct model outputs. Our in-depth study of the Big-Math-RL-Verified dataset reveals that over 38% of model-generated responses suffer from false negatives, where the verifier fails to recognize correct answers. We show, both empirically and theoretically, that these false negatives severely impair RL training by depriving the model of informative gradient signals and slowing convergence. To mitigate this, we propose tinyV, a lightweight LLM-based verifier that augments existing rule-based methods, which dynamically identifies potential false negatives and recovers valid responses to produce more accurate reward estimates. Across multiple math-reasoning benchmarks, integrating TinyV boosts pass rates by up to 10% and accelerates convergence relative to the baseline. Our findings highlight the critical importance of addressing verifier false negatives and offer a practical approach to improve RL-based fine-tuning of LLMs. Our code is available at https://github.com/uw-nsl/TinyV.

Reinforcement learning (RL) with tree search has demonstrated superior performance in traditional reasoning tasks. Compared to conventional independent chain sampling strategies with outcome supervision, tree search enables better exploration of the reasoning space and provides dense, on-policy process rewards during RL training but remains under-explored in On-Policy LLM RL. We propose TreeRL, a reinforcement learning framework that directly incorporates on-policy tree search for RL training. Our approach includes intermediate supervision and eliminates the need for a separate reward model training. Existing approaches typically train a separate process reward model, which can suffer from distribution mismatch and reward hacking. We also introduce a cost-effective tree search approach that achieves higher search efficiency under the same generation token budget by strategically branching from high-uncertainty intermediate steps rather than using random branching. Experiments on challenging math and code reasoning benchmarks demonstrate that TreeRL achieves superior performance compared to traditional ChainRL, highlighting the potential of tree search for LLM. TreeRL is open-sourced at https://github.com/THUDM/TreeRL.

While many real-world problems that might benefit from reinforcement learning, these problems rarely fit into the MDP mold: interacting with the environment is often expensive and specifying reward functions is challenging. Motivated by these challenges, prior work has developed data-driven approaches that learn entirely from samples from the transition dynamics and examples of high-return states. These methods typically learn a reward function from high-return states, use that reward function to label the transitions, and then apply an offline RL algorithm to these transitions. While these methods can achieve good results on many tasks, they can be complex, often requiring regularization and temporal difference updates. In this paper, we propose a method for offline, example-based control that learns an implicit model of multi-step transitions, rather than a reward function. We show that this implicit model can represent the Q-values for the example-based control problem. Across a range of state-based and image-based offline control tasks, our method outperforms baselines that use learned reward functions; additional experiments demonstrate improved robustness and scaling with dataset size.

When language models (LMs) are trained via reinforcement learning (RL) to generate natural language "reasoning chains", their performance improves on a variety of difficult question answering tasks. Today, almost all successful applications of RL for reasoning use binary reward functions that evaluate the correctness of LM outputs. Because such reward functions do not penalize guessing or low-confidence outputs, they often have the unintended side-effect of degrading calibration and increasing the rate at which LMs generate incorrect responses (or "hallucinate") in other problem domains. This paper describes RLCR (Reinforcement Learning with Calibration Rewards), an approach to training reasoning models that jointly improves accuracy and calibrated confidence estimation. During RLCR, LMs generate both predictions and numerical confidence estimates after reasoning. They are trained to optimize a reward function that augments a binary correctness score with a Brier score -- a scoring rule for confidence estimates that incentivizes calibrated prediction. We first prove that this reward function (or any analogous reward function that uses a bounded, proper scoring rule) yields models whose predictions are both accurate and well-calibrated. We next show that across diverse datasets, RLCR substantially improves calibration with no loss in accuracy, on both in-domain and out-of-domain evaluations -- outperforming both ordinary RL training and classifiers trained to assign post-hoc confidence scores. While ordinary RL hurts calibration, RLCR improves it. Finally, we demonstrate that verbalized confidence can be leveraged at test time to improve accuracy and calibration via confidence-weighted scaling methods. Our results show that explicitly optimizing for calibration can produce more generally reliable reasoning models.

Reinforcement learning with verifiable rewards (RLVR) has emerged as a powerful paradigm for enhancing the reasoning capabilities of large language models (LLMs). Unlike traditional RL approaches, RLVR leverages rule-based feedback to guide LLMs in generating and refining complex reasoning chains -- a process critically dependent on effective exploration strategies. While prior work has demonstrated RLVR's empirical success, the fundamental mechanisms governing LLMs' exploration behaviors remain underexplored. This technical report presents a systematic investigation of exploration capacities in RLVR, covering four main aspects: (1) exploration space shaping, where we develop quantitative metrics to characterize LLMs' capability boundaries; (2) entropy-performance exchange, analyzed across training stages, individual instances, and token-level patterns; and (3) RL performance optimization, examining methods to effectively translate exploration gains into measurable improvements. By unifying previously identified insights with new empirical evidence, this work aims to provide a foundational framework for advancing RLVR systems.

Human intelligence involves metacognitive abilities like self-regulation, recognizing limitations, and seeking assistance only when needed. While LLM Agents excel in many domains, they often lack this awareness. Overconfident agents risk catastrophic failures, while those that seek help excessively hinder efficiency. A key challenge is enabling agents with a limited intervention budget C is to decide when to request assistance. In this paper, we propose an offline framework that trains a "helper" policy to request interventions, such as more powerful models or test-time compute, by combining LLM-based process reward models (PRMs) with tabular reinforcement learning. Using state transitions collected offline, we score optimal intervention timing with PRMs and train the helper model on these labeled trajectories. This offline approach significantly reduces costly intervention calls during training. Furthermore, the integration of PRMs with tabular RL enhances robustness to off-policy data while avoiding the inefficiencies of deep RL. We empirically find that our method delivers optimal helper behavior.

Large language models (LLMs) have notably progressed in multi-step and long-chain reasoning. However, extending their reasoning capabilities to encompass deep interactions with search remains a non-trivial challenge, as models often fail to identify optimal reasoning-search interaction trajectories, resulting in suboptimal responses. We propose R-Search, a novel reinforcement learning framework for Reasoning-Search integration, designed to enable LLMs to autonomously execute multi-step reasoning with deep search interaction, and learn optimal reasoning search interaction trajectories via multi-reward signals, improving response quality in complex logic- and knowledge-intensive tasks. R-Search guides the LLM to dynamically decide when to retrieve or reason, while globally integrating key evidence to enhance deep knowledge interaction between reasoning and search. During RL training, R-Search provides multi-stage, multi-type rewards to jointly optimize the reasoning-search trajectory. Experiments on seven datasets show that R-Search outperforms advanced RAG baselines by up to 32.2% (in-domain) and 25.1% (out-of-domain). The code and data are available at https://github.com/QingFei1/R-Search.

Recent advances in reasoning capabilities of large language models (LLMs) are largely driven by reinforcement learning (RL), yet the underlying parameter dynamics during RL training remain poorly understood. This work identifies two fundamental properties of RL-induced parameter updates in LLMs: (1) Rank-1 Dominance, where the top singular subspace of the parameter update matrix nearly fully determines reasoning improvements, recovering over 99\% of performance gains; and (2) Rank-1 Linear Dynamics, where this dominant subspace evolves linearly throughout training, enabling accurate prediction from early checkpoints. Extensive experiments across 8 LLMs and 7 algorithms validate the generalizability of these properties. More importantly, based on these findings, we propose AlphaRL, a plug-in acceleration framework that extrapolates the final parameter update using a short early training window, achieving up to 2.5 speedup while retaining \textgreater 96\% of reasoning performance without extra modules or hyperparameter tuning. This positions our finding as a versatile and practical tool for large-scale RL, opening a path toward principled, interpretable, and efficient training paradigm for LLMs.

We study risk-sensitive Reinforcement Learning (RL), where we aim to maximize the Conditional Value at Risk (CVaR) with a fixed risk tolerance tau. Prior theoretical work studying risk-sensitive RL focuses on the tabular Markov Decision Processes (MDPs) setting. To extend CVaR RL to settings where state space is large, function approximation must be deployed. We study CVaR RL in low-rank MDPs with nonlinear function approximation. Low-rank MDPs assume the underlying transition kernel admits a low-rank decomposition, but unlike prior linear models, low-rank MDPs do not assume the feature or state-action representation is known. We propose a novel Upper Confidence Bound (UCB) bonus-driven algorithm to carefully balance the interplay between exploration, exploitation, and representation learning in CVaR RL. We prove that our algorithm achieves a sample complexity of Oleft(H^7 A^2 d^4{tau^2 epsilon^2}right) to yield an epsilon-optimal CVaR, where H is the length of each episode, A is the capacity of action space, and d is the dimension of representations. Computational-wise, we design a novel discretized Least-Squares Value Iteration (LSVI) algorithm for the CVaR objective as the planning oracle and show that we can find the near-optimal policy in a polynomial running time with a Maximum Likelihood Estimation oracle. To our knowledge, this is the first provably efficient CVaR RL algorithm in low-rank MDPs.

Large language models (LLMs) fine-tuned by reinforcement learning from human feedback (RLHF) are becoming more widely deployed. We coin the term Implicit Reward Model (IRM) to refer to the changes that occur to an LLM during RLHF that result in high-reward generations. We interpret IRMs, and measure their divergence from the RLHF reward model used in the fine-tuning process that induced them. By fitting a linear function to an LLM's IRM, a reward model with the same type signature as the RLHF reward model is constructed, allowing for direct comparison. Additionally, we validate our construction of the IRM through cross-comparison with classifications of features generated by an LLM based on their relevance to the RLHF reward model. Better comprehending IRMs can help minimize discrepencies between LLM behavior and training objectives, which we believe to be an essential component of the safety and alignment of LLMs.

We introduce SAIL-RL, a reinforcement learning (RL) post-training framework that enhances the reasoning capabilities of multimodal large language models (MLLMs) by teaching them when and how to think. Existing approaches are limited by outcome-only supervision, which rewards correct answers without ensuring sound reasoning, and by uniform thinking strategies, which often lead to overthinking on simple tasks and underthinking on complex ones. SAIL-RL addresses these challenges with a dual reward system: the Thinking Reward, which evaluates reasoning quality through factual grounding, logical coherence, and answer consistency, and the Judging Reward, which adaptively determines whether deep reasoning or direct answering is appropriate. Experiments on the state-of-the-art SAIL-VL2 show that SAIL-RL improves reasoning and multimodal understanding benchmarks at both 4B and 8B scales, achieving competitive performance against commercial closed-source models such as GPT-4o, and substantially reduces hallucinations, establishing it as a principled framework for building more reliable and adaptive MLLMs. The code will be available at https://github.com/BytedanceDouyinContent/SAIL-RL.

We propose a reinforcement learning (RL) framework under a broad class of risk objectives, characterized by convex scoring functions. This class covers many common risk measures, such as variance, Expected Shortfall, entropic Value-at-Risk, and mean-risk utility. To resolve the time-inconsistency issue, we consider an augmented state space and an auxiliary variable and recast the problem as a two-state optimization problem. We propose a customized Actor-Critic algorithm and establish some theoretical approximation guarantees. A key theoretical contribution is that our results do not require the Markov decision process to be continuous. Additionally, we propose an auxiliary variable sampling method inspired by the alternating minimization algorithm, which is convergent under certain conditions. We validate our approach in simulation experiments with a financial application in statistical arbitrage trading, demonstrating the effectiveness of the algorithm.

A prominent challenge of offline reinforcement learning (RL) is the issue of hidden confounding: unobserved variables may influence both the actions taken by the agent and the observed outcomes. Hidden confounding can compromise the validity of any causal conclusion drawn from data and presents a major obstacle to effective offline RL. In the present paper, we tackle the problem of hidden confounding in the nonidentifiable setting. We propose a definition of uncertainty due to hidden confounding bias, termed delphic uncertainty, which uses variation over world models compatible with the observations, and differentiate it from the well-known epistemic and aleatoric uncertainties. We derive a practical method for estimating the three types of uncertainties, and construct a pessimistic offline RL algorithm to account for them. Our method does not assume identifiability of the unobserved confounders, and attempts to reduce the amount of confounding bias. We demonstrate through extensive experiments and ablations the efficacy of our approach on a sepsis management benchmark, as well as on electronic health records. Our results suggest that nonidentifiable hidden confounding bias can be mitigated to improve offline RL solutions in practice.

Accurate prediction of major adverse cardiovascular events recurrence risk in acute myocardial infarction patients based on postoperative cardiac MRI and associated clinical notes is crucial for precision treatment and personalized intervention. Existing methods primarily focus on risk stratification capability while overlooking the need for intermediate robust reasoning and model interpretability in clinical practice. Moreover, end-to-end risk prediction using LLM/VLM faces significant challenges due to data limitations and modeling complexity. To bridge this gap, we propose CardioCoT, a novel two-stage hierarchical reasoning-enhanced survival analysis framework designed to enhance both model interpretability and predictive performance. In the first stage, we employ an evidence-augmented self-refinement mechanism to guide LLM/VLMs in generating robust hierarchical reasoning trajectories based on associated radiological findings. In the second stage, we integrate the reasoning trajectories with imaging data for risk model training and prediction. CardioCoT demonstrates superior performance in MACE recurrence risk prediction while providing interpretable reasoning processes, offering valuable insights for clinical decision-making.

We show that reinforcement learning with verifiable reward using one training example (1-shot RLVR) is effective in incentivizing the math reasoning capabilities of large language models (LLMs). Applying RLVR to the base model Qwen2.5-Math-1.5B, we identify a single example that elevates model performance on MATH500 from 36.0% to 73.6%, and improves the average performance across six common mathematical reasoning benchmarks from 17.6% to 35.7%. This result matches the performance obtained using the 1.2k DeepScaleR subset (MATH500: 73.6%, average: 35.9%), which includes the aforementioned example. Similar substantial improvements are observed across various models (Qwen2.5-Math-7B, Llama3.2-3B-Instruct, DeepSeek-R1-Distill-Qwen-1.5B), RL algorithms (GRPO and PPO), and different math examples (many of which yield approximately 30% or greater improvement on MATH500 when employed as a single training example). In addition, we identify some interesting phenomena during 1-shot RLVR, including cross-domain generalization, increased frequency of self-reflection, and sustained test performance improvement even after the training accuracy has saturated, a phenomenon we term post-saturation generalization. Moreover, we verify that the effectiveness of 1-shot RLVR primarily arises from the policy gradient loss, distinguishing it from the "grokking" phenomenon. We also show the critical role of promoting exploration (e.g., by adding entropy loss with an appropriate coefficient) in 1-shot RLVR training. As a bonus, we observe that applying entropy loss alone, without any outcome reward, significantly enhances Qwen2.5-Math-1.5B's performance on MATH500 by 27.4%. These findings can inspire future work on RLVR data efficiency and encourage a re-examination of both recent progress and the underlying mechanisms in RLVR. Our code, model, and data are open source at https://github.com/ypwang61/One-Shot-RLVR

Extending Reinforcement Learning with Verifiable Rewards (RLVR) to real-world tasks often requires balancing objective and subjective evaluation criteria. However, many such tasks lack a single, unambiguous ground truth-making it difficult to define reliable reward signals for post-training language models. While traditional preference-based methods offer a workaround, they rely on opaque reward functions that are difficult to interpret and prone to spurious correlations. We introduce Rubrics as Rewards (RaR), a framework that uses structured, checklist-style rubrics as interpretable reward signals for on-policy training with GRPO. Our best RaR method yields up to a 28% relative improvement on HealthBench-1k compared to simple Likert-based approaches, while matching or surpassing the performance of reward signals derived from expert-written references. By treating rubrics as structured reward signals, we show that RaR enables smaller-scale judge models to better align with human preferences and sustain robust performance across model scales.

Model-based methods have recently shown promising for offline reinforcement learning (RL), aiming to learn good policies from historical data without interacting with the environment. Previous model-based offline RL methods learn fully connected nets as world-models that map the states and actions to the next-step states. However, it is sensible that a world-model should adhere to the underlying causal effect such that it will support learning an effective policy generalizing well in unseen states. In this paper, We first provide theoretical results that causal world-models can outperform plain world-models for offline RL by incorporating the causal structure into the generalization error bound. We then propose a practical algorithm, oFfline mOdel-based reinforcement learning with CaUsal Structure (FOCUS), to illustrate the feasibility of learning and leveraging causal structure in offline RL. Experimental results on two benchmarks show that FOCUS reconstructs the underlying causal structure accurately and robustly. Consequently, it performs better than the plain model-based offline RL algorithms and other causal model-based RL algorithms.

Supervised fine-tuning (SFT) and reinforcement learning (RL) are widely used post-training techniques for foundation models. However, their roles in enhancing model generalization capabilities remain unclear. This paper studies the difference between SFT and RL on generalization and memorization, focusing on text-based rule variants and visual variants. We introduce GeneralPoints, an arithmetic reasoning card game, and adopt V-IRL, a real-world navigation environment, to assess how models trained with SFT and RL generalize to unseen variants in both textual and visual domains. We show that RL, especially when trained with an outcome-based reward, generalizes across both rule-based textual and visual variants. SFT, in contrast, tends to memorize training data and struggles to generalize out-of-distribution scenarios. Further analysis reveals that RL improves the model's underlying visual recognition capabilities, contributing to its enhanced generalization in the visual domain. Despite RL's superior generalization, we show that SFT remains essential for effective RL training; SFT stabilizes the model's output format, enabling subsequent RL to achieve its performance gains. These findings demonstrates the capability of RL for acquiring generalizable knowledge in complex, multi-modal tasks.

Reinforcement learning from human feedback (RLHF) has become a powerful post-training paradigm for aligning large language models with human preferences. A core challenge in RLHF is constructing accurate reward signals, where the conventional Bradley-Terry reward models (BT RMs) often suffer from sensitivity to data size and coverage, as well as vulnerability to reward hacking. Generative reward models (GenRMs) offer a more robust alternative by generating chain-of-thought (CoT) rationales followed by a final reward. However, existing GenRMs rely on shallow, vertically scaled reasoning, limiting their capacity to handle nuanced or complex (e.g., reasoning-intensive) tasks. Moreover, their pairwise preference outputs are incompatible with standard RLHF algorithms that require pointwise reward signals. In this work, we introduce Think-RM, a training framework that enables long-horizon reasoning in GenRMs by modeling an internal thinking process. Rather than producing structured, externally provided rationales, Think-RM generates flexible, self-guided reasoning traces that support advanced capabilities such as self-reflection, hypothetical reasoning, and divergent reasoning. To elicit these reasoning abilities, we first warm-up the models by supervised fine-tuning (SFT) over long CoT data. We then further improve the model's long-horizon abilities by rule-based reinforcement learning (RL). In addition, we propose a novel pairwise RLHF pipeline that directly optimizes policies using pairwise preference rewards, eliminating the need for pointwise reward conversion and enabling more effective use of Think-RM outputs. Experiments show that Think-RM achieves state-of-the-art results on RM-Bench, outperforming both BT RM and vertically scaled GenRM by 8%. When combined with our pairwise RLHF pipeline, it demonstrates superior end-policy performance compared to traditional approaches.

Direct Alignment Algorithms (DAAs) simplify language model alignment by replacing reinforcement learning (RL) and reward modeling (RM) in Reinforcement Learning from Human Feedback (RLHF) with direct policy optimization. DAAs can be classified by their ranking losses (pairwise vs. pointwise), by the rewards used in those losses (e.g., likelihood ratios of policy and reference policy, or odds ratios), or by whether a Supervised Fine-Tuning (SFT) phase is required (two-stage vs. one-stage). We first show that one-stage methods underperform two-stage methods. To address this, we incorporate an explicit SFT phase and introduce the beta parameter, controlling the strength of preference optimization, into single-stage ORPO and ASFT. These modifications improve their performance in Alpaca Eval 2 by +3.46 (ORPO) and +8.27 (ASFT), matching two-stage methods like DPO. Further analysis reveals that the key factor is whether the approach uses pairwise or pointwise objectives, rather than the specific implicit reward or loss function. These results highlight the importance of careful evaluation to avoid premature claims of performance gains or overall superiority in alignment algorithms.

When applying offline reinforcement learning (RL) in healthcare scenarios, the out-of-distribution (OOD) issues pose significant risks, as inappropriate generalization beyond clinical expertise can result in potentially harmful recommendations. While existing methods like conservative Q-learning (CQL) attempt to address the OOD issue, their effectiveness is limited by only constraining action selection by suppressing uncertain actions. This action-only regularization imitates clinician actions that prioritize short-term rewards, but it fails to regulate downstream state trajectories, thereby limiting the discovery of improved long-term treatment strategies. To safely improve policy beyond clinician recommendations while ensuring that state-action trajectories remain in-distribution, we propose Offline Guarded Safe Reinforcement Learning (OGSRL), a theoretically grounded model-based offline RL framework. OGSRL introduces a novel dual constraint mechanism for improving policy with reliability and safety. First, the OOD guardian is established to specify clinically validated regions for safe policy exploration. By constraining optimization within these regions, it enables the reliable exploration of treatment strategies that outperform clinician behavior by leveraging the full patient state history, without drifting into unsupported state-action trajectories. Second, we introduce a safety cost constraint that encodes medical knowledge about physiological safety boundaries, providing domain-specific safeguards even in areas where training data might contain potentially unsafe interventions. Notably, we provide theoretical guarantees on safety and near-optimality: policies that satisfy these constraints remain in safe and reliable regions and achieve performance close to the best possible policy supported by the data.

Reward modeling is essential for aligning large language models (LLMs) with human preferences, especially through reinforcement learning from human feedback (RLHF). To provide accurate reward signals, a reward model (RM) should stimulate deep thinking and conduct interpretable reasoning before assigning a score or a judgment. However, existing RMs either produce opaque scalar scores or directly generate the prediction of a preferred answer, making them struggle to integrate natural language critiques, thus lacking interpretability. Inspired by recent advances of long chain-of-thought (CoT) on reasoning-intensive tasks, we hypothesize and validate that integrating reasoning capabilities into reward modeling significantly enhances RM's interpretability and performance. In this work, we introduce a new class of generative reward models -- Reasoning Reward Models (ReasRMs) -- which formulate reward modeling as a reasoning task. We propose a reasoning-oriented training pipeline and train a family of ReasRMs, RM-R1. The training consists of two key stages: (1) distillation of high-quality reasoning chains and (2) reinforcement learning with verifiable rewards. RM-R1 improves LLM rollouts by self-generating reasoning traces or chat-specific rubrics and evaluating candidate responses against them. Empirically, our models achieve state-of-the-art or near state-of-the-art performance of generative RMs across multiple comprehensive reward model benchmarks, outperforming much larger open-weight models (e.g., Llama3.1-405B) and proprietary ones (e.g., GPT-4o) by up to 13.8%. Beyond final performance, we perform thorough empirical analysis to understand the key ingredients of successful ReasRM training. To facilitate future research, we release six ReasRM models along with code and data at https://github.com/RM-R1-UIUC/RM-R1.

Reinforcement Learning with Verifiable Rewards (RLVR) has demonstrated success in enhancing LLM reasoning capabilities, but remains limited to single-turn interactions without tool integration. While recent Agentic Reinforcement Learning with Tool use (ARLT) approaches have emerged to address multi-turn tool interactions, existing works develop task-specific codebases that suffer from fragmentation, synchronous execution bottlenecks, and limited extensibility across domains. These inefficiencies hinder broader community adoption and algorithmic innovation. We introduce VerlTool, a unified and modular framework that addresses these limitations through systematic design principles. VerlTool provides four key contributions: (1) upstream alignment with VeRL ensuring compatibility and simplified maintenance, (2) unified tool management via standardized APIs supporting diverse modalities including code execution, search, SQL databases, and vision processing, (3) asynchronous rollout execution achieving near 2times speedup by eliminating synchronization bottlenecks, and (4) comprehensive evaluation demonstrating competitive performance across 6 ARLT domains. Our framework formalizes ARLT as multi-turn trajectories with multi-modal observation tokens (text/image/video), extending beyond single-turn RLVR paradigms. We train and evaluate models on mathematical reasoning, knowledge QA, SQL generation, visual reasoning, web search, and software engineering tasks, achieving results comparable to specialized systems while providing unified training infrastructure. The modular plugin architecture enables rapid tool integration requiring only lightweight Python definitions, significantly reducing development overhead and providing a scalable foundation for tool-augmented RL research. Our code is open-sourced at https://github.com/TIGER-AI-Lab/verl-tool.

Reinforcement Learning with Verifiable Rewards (RLVR) has recently emerged as a powerful paradigm for facilitating the self-improvement of large language models (LLMs), particularly in the domain of complex reasoning tasks. However, prevailing on-policy RL methods often contend with significant training instability and inefficiency. This is primarily due to a capacity-difficulty mismatch, where the complexity of training data frequently outpaces the model's current capabilities, leading to critically sparse reward signals and stalled learning progress. This challenge is particularly acute for smaller, more resource-efficient LLMs. To overcome this, we introduce the Guided Hybrid Policy Optimization (GHPO), a novel difficulty-aware reinforcement learning framework. GHPO dynamically calibrates task difficulty by employing adaptive prompt refinement to provide targeted guidance. This unique approach adaptively balances direct imitation learning for problems currently beyond the model's reach with exploration-based reinforcement learning for more manageable tasks, effectively creating a smooth and optimized learning curriculum. Extensive experiments demonstrate that GHPO achieves an average performance gain of approximately 5% across six challenging mathematics benchmarks, consistently outperforming strong on-policy reinforcement learning and curriculum learning baselines. Further analysis confirms that our framework significantly enhances both training stability and final reasoning performance, thus offering a scalable and efficient solution for developing powerful and robust reasoning models.

Recent advances in large language models have been driven by reinforcement learning (RL)-style post-training, which improves reasoning by optimizing model outputs based on reward or preference signals. GRPO-style approaches implement this by using self-generated samples labeled by an outcome-based verifier. However, these methods depend heavily on the model's initial ability to produce positive samples. They primarily refine what the model already knows (distribution sharpening) rather than enabling the model to solve problems where it initially fails. This limitation is especially problematic in early-stage RL training and on challenging reasoning tasks, where positive samples are unlikely to be generated. To unlock reasoning ability in such settings, the model must explore new reasoning trajectories beyond its current output distribution. Such exploration requires access to sufficiently good positive samples to guide the learning. While expert demonstrations seem like a natural solution, we find that they are often ineffective in RL post-training. Instead, we identify two key properties of effective positive samples: they should (1) be likely under the current policy, and (2) increase the model's likelihood of predicting the correct answer. Based on these insights, we propose Self-Explanation Policy Optimization (ExPO)-a simple and modular framework that generates such samples by conditioning on the ground-truth answer. ExPO enables efficient exploration and guides the model to produce reasoning trajectories more aligned with its policy than expert-written CoTs, while ensuring higher quality than its own (incorrect) samples. Experiments show that ExPO improves both learning efficiency and final performance on reasoning benchmarks, surpassing expert-demonstration-based methods in challenging settings such as MATH level-5, where the model initially struggles the most.

Generative reward models (also known as LLMs-as-judges), which use large language models (LLMs) to evaluate answer quality, are increasingly adopted in reinforcement learning with verifiable rewards (RLVR). They are often preferred over rigid rule-based metrics, especially for complex reasoning tasks involving free-form outputs. In this paradigm, an LLM is typically prompted to compare a candidate answer against a ground-truth reference and assign a binary reward indicating correctness. Despite the seeming simplicity of this comparison task, we find that generative reward models exhibit surprising vulnerabilities to superficial manipulations: non-word symbols (e.g., ":" or ".") or reasoning openers like "Thought process:" and "Let's solve this problem step by step." can often lead to false positive rewards. We demonstrate that this weakness is widespread across LLMs, datasets, and prompt formats, posing a serious threat for core algorithmic paradigms that rely on generative reward models, such as rejection sampling, preference optimization, and RLVR. To mitigate this issue, we introduce a simple yet effective data augmentation strategy and train a new generative reward model with substantially improved robustness. Our findings highlight the urgent need for more reliable LLM-based evaluation methods. We release our robust, general-domain reward model and its synthetic training data at https://huggingface.co/sarosavo/Master-RM and https://huggingface.co/datasets/sarosavo/Master-RM.

Recent Large Language Models (LLMs) and Large Vision-Language Models (LVLMs) increasingly use Reinforcement Learning (RL) for post-pretraining, such as RL with Verifiable Rewards (RLVR) for objective tasks and RL from Human Feedback (RLHF) for subjective tasks. However, RLHF incurs high costs and potential reward-policy mismatch due to reliance on human preferences, while RLVR still wastes supervision by discarding rollouts and correctness signals after each update. To address these challenges, we introduce the Synergistic Policy And Reward Co-Evolving Framework (SPARK), an efficient, on-policy, and stable method that builds on RLVR. Instead of discarding rollouts and correctness data, SPARK recycles this valuable information to simultaneously train the model itself as a generative reward model. This auxiliary training uses a mix of objectives, such as pointwise reward score, pairwise comparison, and evaluation conditioned on further-reflection responses, to teach the model to evaluate and improve its own responses. Our process eliminates the need for a separate reward model and costly human preference data. SPARK creates a positive co-evolving feedback loop: improved reward accuracy yields better policy gradients, which in turn produce higher-quality rollouts that further refine the reward model. Our unified framework supports test-time scaling via self-reflection without external reward models and their associated costs. We show that SPARK achieves significant performance gains on multiple LLM and LVLM models and multiple reasoning, reward models, and general benchmarks. For example, SPARK-VL-7B achieves an average 9.7% gain on 7 reasoning benchmarks, 12.1% on 2 reward benchmarks, and 1.5% on 8 general benchmarks over the baselines, demonstrating robustness and broad generalization.

Offline reinforcement learning (RL) has progressed with return-conditioned supervised learning (RCSL), but its lack of stitching ability remains a limitation. We introduce Q-Aided Conditional Supervised Learning (QCS), which effectively combines the stability of RCSL with the stitching capability of Q-functions. By analyzing Q-function over-generalization, which impairs stable stitching, QCS adaptively integrates Q-aid into RCSL's loss function based on trajectory return. Empirical results show that QCS significantly outperforms RCSL and value-based methods, consistently achieving or exceeding the maximum trajectory returns across diverse offline RL benchmarks.

Reinforcement Learning with Verifiable Reward (RLVR) effectively solves complex tasks but demands extremely long context lengths during training, leading to substantial computational costs. While multi-stage training can partially mitigate this, starting with overly short contexts often causes irreversible performance degradation, ultimately failing to reduce overall training compute significantly. In this paper, we introduce **T**hinking-**F**ree **P**olicy **I**nitialization (**TFPI**), a simple yet effective adaptation to RLVR that bridges long Chain-of-Thought (CoT) distillation and standard RLVR. TFPI employs a simple *ThinkFree* operation, explicitly discarding the thinking content via a direct *</think>* append, to reduce token usage during inference. Training with *ThinkFree*-adapted inputs improves performance and lowers token consumption, even in the original slow-thinking mode. Extensive experiments across various benchmarks have shown that TFPI accelerates RL convergence, achieves a higher performance ceiling, and yields more token-efficient reasoning models without specialized rewards or complex training designs. With TFPI only, we train a 4B model to reach 89.0% accuracy on AIME24 and 65.5% on LiveCodeBench using less than 4K H20 hours.

Recent advances in large language models (LLMs) have demonstrated significant progress in performing complex tasks. While Reinforcement Learning from Human Feedback (RLHF) has been effective in aligning LLMs with human preferences, it is susceptible to spurious correlations in reward modeling. Consequently, it often introduces biases-such as length bias, sycophancy, conceptual bias, and discrimination that hinder the model's ability to capture true causal relationships. To address this, we propose a novel causal reward modeling approach that integrates causal inference to mitigate these spurious correlations. Our method enforces counterfactual invariance, ensuring reward predictions remain consistent when irrelevant variables are altered. Through experiments on both synthetic and real-world datasets, we show that our approach mitigates various types of spurious correlations effectively, resulting in more reliable and fair alignment of LLMs with human preferences. As a drop-in enhancement to the existing RLHF workflow, our causal reward modeling provides a practical way to improve the trustworthiness and fairness of LLM finetuning.

Reinforcement Learning with Verifiable Rewards (RLVR) has improved the reasoning abilities of Large Language Models (LLMs) by using rule-based binary feedback, helping to mitigate reward hacking. However, current RLVR methods typically treat whole responses as single actions, assigning the same reward to every token. This coarse-grained feedback hampers precise credit assignment, making it hard for models to identify which reasoning steps lead to success or failure, and often results in suboptimal policies and inefficient learning. Methods like PPO provide credit assignment through value estimation, but often yield inaccurate and unverifiable signals due to limited sampling. On the other hand, methods using Process Reward Models can provide step-by-step judgments for each reasoning step, but they require high-quality process supervision labels and are time-consuming when applied in online reinforcement learning (RL). To overcome these limitations, we introduce a simple but efficient method Credit Assignment Policy Optimization (CAPO). Given a reasoning response rollout from the policy model, CAPO directly leverages an off-the-shelf, general-purpose LLM as a Generative Process Reward Model (LLM-as-GenPRM) to generate all step-wise critique by one pass, thereby providing verifiable token-level rewards to refine the tokens that were originally assigned identical rule-based rewards. This enables more fine-grained credit assignment in an effective way. Furthermore, to enhance the accuracy and robustness of CAPO, we employ voting mechanisms that scale with the number of generated critiques. Extensive experiments using different backbones like Llama and Qwen models and in different sizes show that CAPO consistently outperforms supervised learning-based and RL-based fine-tuning methods across six challenging mathematical benchmarks and three out-of-domain benchmarks.

Reinforcement learning (RL) has played an important role in improving the reasoning ability of large language models (LLMs). Some studies apply RL directly to smaller base models (known as zero-RL) and also achieve notable progress. However, in this paper, we show that using only 920 examples, a simple distillation method based on the base model can clearly outperform zero-RL, which typically requires much more data and computational cost. By analyzing the token frequency in model outputs, we find that the distilled model shows more flexible reasoning. It uses anthropomorphic tokens and logical connectors much more often than the zero-RL model. Further analysis reveals that distillation enhances the presence of two advanced cognitive behaviors: Multi-Perspective Thinking or Attempting and Metacognitive Awareness. Frequent occurrences of these two advanced cognitive behaviors give rise to flexible reasoning, which is essential for solving complex reasoning problems, while zero-RL fails to significantly boost the frequency of these behaviors.

Our motivation is to shed light the performance of the widely popular "R-Learner." Like many other methods for estimating conditional average treatment effects (CATEs), R-Learning can be expressed as a weighted pseudo-outcome regression (POR). Previous comparisons of POR techniques have paid careful attention to the choice of pseudo-outcome transformation. However, we argue that the dominant driver of performance is actually the choice of weights. Specifically, we argue that R-Learning implicitly performs an inverse-variance weighted form of POR. These weights stabilize the regression and allow for convenient simplifications of bias terms.

Large language models (LLMs) are increasingly trained with reinforcement learning (RL) as autonomous agents that reason and act over long horizons in interactive environments. However, sparse and sometimes unverifiable rewards make temporal credit assignment extremely challenging. Recent work attempts to integrate process supervision into agent learning but suffers from biased annotation, reward hacking, high-variance from overly fine-grained signals or failtures when state overlap is rare. We therefore introduce Online Process Reward Learning (OPRL), a general credit-assignment strategy for agentic RL that integrates seamlessly with standard on-policy algorithms without relying on additional rollouts or explicit step labels. In OPRL, we optimize an implicit process reward model (PRM) alternately with the agent's policy to transform trajectory preferences into implicit step rewards through a trajectory-based DPO objective. These step rewards are then used to compute step-level advantages, which are combined with episode-level advantages from outcome rewards for policy update, creating a self-reinforcing loop. Theoretical findings guarantee that the learned step rewards are consistent with trajectory preferences and act as potential-based shaping rewards, providing bounded gradients to stabilize training. Empirically, we evaluate OPRL on three distinct agent benmarks, including WebShop and VisualSokoban, as well as open-ended social interactions with unverfiable rewards in SOTOPIA. Crucially, OPRL shows superior performance over frontier LLMs and strong RL baselines across domains, achieving state-of-the-art results with higher sample-efficiency and lower variance during training. Further analysis also demonstrates the efficient exploration by OPRL using fewer actions, underscoring its potential for agentic learning in real-world scenarios.

Process Reward Modeling (PRM) is critical for complex reasoning and decision-making tasks where the accuracy of intermediate steps significantly influences the overall outcome. Existing PRM approaches, primarily framed as classification problems, employ cross-entropy loss to independently evaluate each step's correctness. This method can lead to suboptimal reward distribution and does not adequately address the interdependencies among steps. To address these limitations, we introduce the Process Q-value Model (PQM), a novel framework that redefines PRM in the context of a Markov Decision Process. PQM optimizes Q-value rankings based on a novel comparative loss function, enhancing the model's ability to capture the intricate dynamics among sequential decisions. This approach provides a more granular and theoretically grounded methodology for process rewards. Our extensive empirical evaluations across various sampling policies, language model backbones, and multi-step reasoning benchmarks show that PQM outperforms classification-based PRMs. The effectiveness of the comparative loss function is highlighted in our comprehensive ablation studies, confirming PQM's practical efficacy and theoretical advantage.

Research on applications of Reinforcement Learning (RL) to Large Language Models (LLMs) has mostly been focused on single-turn problems, such as mathematical reasoning or single-shot code generation. While these problems can be viewed as token-level multi-turn MDPs, this view corresponds to a degenerate case of multi-turn interaction where the environment provides no feedback. This contrasts with many real-world domains, such as software engineering (SWE), which require rich multi-turn interactions with a stateful environment that responds to each action with a non-trivial observation. To bridge this gap, we demonstrate the successful application of RL to this general regime. Using a modified Decoupled Advantage Policy Optimization (DAPO) algorithm, we train an agent based on Qwen2.5-72B-Instruct to solve real-world software engineering tasks. Our approach increases the agent's success rate on the SWE-bench Verified benchmark from a 20% rejection fine-tuned baseline to 39%, without relying on any teacher models. On SWE-rebench, our agent matches or outperforms leading open-weight models such as DeepSeek-V3-0324 and Qwen3-235B-A22B using an identical scaffolding, offering a viable path toward building more capable autonomous agents for complex real-world problems based on open models.

Recent work has demonstrated the effectiveness of formulating decision making as a supervised learning problem on offline-collected trajectories. However, the benefits of performing sequence modeling on trajectory data is not yet clear. In this work we investigate if sequence modeling has the capability to condense trajectories into useful representations that can contribute to policy learning. To achieve this, we adopt a two-stage framework that first summarizes trajectories with sequence modeling techniques, and then employs these representations to learn a policy along with a desired goal. This design allows many existing supervised offline RL methods to be considered as specific instances of our framework. Within this framework, we introduce Goal-Conditioned Predicitve Coding (GCPC), an approach that brings powerful trajectory representations and leads to performant policies. We conduct extensive empirical evaluations on AntMaze, FrankaKitchen and Locomotion environments, and observe that sequence modeling has a significant impact on some decision making tasks. In addition, we demonstrate that GCPC learns a goal-conditioned latent representation about the future, which serves as an "implicit planner", and enables competitive performance on all three benchmarks.

In recent years, reinforcement learning (RL)-based methods for learning driving policies have gained increasing attention in the autonomous driving community and have achieved remarkable progress in various driving scenarios. However, traditional RL approaches rely on manually engineered rewards, which require extensive human effort and often lack generalizability. To address these limitations, we propose VLM-RL, a unified framework that integrates pre-trained Vision-Language Models (VLMs) with RL to generate reward signals using image observation and natural language goals. The core of VLM-RL is the contrasting language goal (CLG)-as-reward paradigm, which uses positive and negative language goals to generate semantic rewards. We further introduce a hierarchical reward synthesis approach that combines CLG-based semantic rewards with vehicle state information, improving reward stability and offering a more comprehensive reward signal. Additionally, a batch-processing technique is employed to optimize computational efficiency during training. Extensive experiments in the CARLA simulator demonstrate that VLM-RL outperforms state-of-the-art baselines, achieving a 10.5\% reduction in collision rate, a 104.6\% increase in route completion rate, and robust generalization to unseen driving scenarios. Furthermore, VLM-RL can seamlessly integrate almost any standard RL algorithms, potentially revolutionizing the existing RL paradigm that relies on manual reward engineering and enabling continuous performance improvements. The demo video and code can be accessed at: https://zilin-huang.github.io/VLM-RL-website.

Reinforcement Learning from Verifiable Rewards (RLVR) has been widely adopted as the de facto method for enhancing the reasoning capabilities of large language models and has demonstrated notable success in verifiable domains like math and competitive programming tasks. However, the efficacy of RLVR diminishes significantly when applied to agentic environments. These settings, characterized by multi-step, complex problem solving, lead to high failure rates even for frontier LLMs, as the reward landscape is too sparse for effective model training via conventional RLVR. In this work, we introduce Agent-RLVR, a framework that makes RLVR effective in challenging agentic settings, with an initial focus on software engineering tasks. Inspired by human pedagogy, Agent-RLVR introduces agent guidance, a mechanism that actively steers the agent towards successful trajectories by leveraging diverse informational cues. These cues, ranging from high-level strategic plans to dynamic feedback on the agent's errors and environmental interactions, emulate a teacher's guidance, enabling the agent to navigate difficult solution spaces and promotes active self-improvement via additional environment exploration. In the Agent-RLVR training loop, agents first attempt to solve tasks to produce initial trajectories, which are then validated by unit tests and supplemented with agent guidance. Agents then reattempt with guidance, and the agent policy is updated with RLVR based on the rewards of these guided trajectories. Agent-RLVR elevates the pass@1 performance of Qwen-2.5-72B-Instruct from 9.4% to 22.4% on SWE-Bench Verified. We find that our guidance-augmented RLVR data is additionally useful for test-time reward model training, shown by further boosting pass@1 to 27.8%. Agent-RLVR lays the groundwork for training agents with RLVR in complex, real-world environments where conventional RL methods struggle.

Risk-sensitive reinforcement learning (RL) has become a popular tool to control the risk of uncertain outcomes and ensure reliable performance in various sequential decision-making problems. While policy gradient methods have been developed for risk-sensitive RL, it remains unclear if these methods enjoy the same global convergence guarantees as in the risk-neutral case. In this paper, we consider a class of dynamic time-consistent risk measures, called Expected Conditional Risk Measures (ECRMs), and derive policy gradient updates for ECRM-based objective functions. Under both constrained direct parameterization and unconstrained softmax parameterization, we provide global convergence and iteration complexities of the corresponding risk-averse policy gradient algorithms. We further test risk-averse variants of REINFORCE and actor-critic algorithms to demonstrate the efficacy of our method and the importance of risk control.

Compositional reinforcement learning is a promising approach for training policies to perform complex long-horizon tasks. Typically, a high-level task is decomposed into a sequence of subtasks and a separate policy is trained to perform each subtask. In this paper, we focus on the problem of training subtask policies in a way that they can be used to perform any task; here, a task is given by a sequence of subtasks. We aim to maximize the worst-case performance over all tasks as opposed to the average-case performance. We formulate the problem as a two agent zero-sum game in which the adversary picks the sequence of subtasks. We propose two RL algorithms to solve this game: one is an adaptation of existing multi-agent RL algorithms to our setting and the other is an asynchronous version which enables parallel training of subtask policies. We evaluate our approach on two multi-task environments with continuous states and actions and demonstrate that our algorithms outperform state-of-the-art baselines.

As Reinforcement Learning (RL) agents are increasingly employed in diverse decision-making problems using reward preferences, it becomes important to ensure that policies learned by these frameworks in mapping observations to a probability distribution of the possible actions are explainable. However, there is little to no work in the systematic understanding of these complex policies in a contrastive manner, i.e., what minimal changes to the policy would improve/worsen its performance to a desired level. In this work, we present COUNTERPOL, the first framework to analyze RL policies using counterfactual explanations in the form of minimal changes to the policy that lead to the desired outcome. We do so by incorporating counterfactuals in supervised learning in RL with the target outcome regulated using desired return. We establish a theoretical connection between Counterpol and widely used trust region-based policy optimization methods in RL. Extensive empirical analysis shows the efficacy of COUNTERPOL in generating explanations for (un)learning skills while keeping close to the original policy. Our results on five different RL environments with diverse state and action spaces demonstrate the utility of counterfactual explanations, paving the way for new frontiers in designing and developing counterfactual policies.

Upside down reinforcement learning (UDRL) flips the conventional use of the return in the objective function in RL upside down, by taking returns as input and predicting actions. UDRL is based purely on supervised learning, and bypasses some prominent issues in RL: bootstrapping, off-policy corrections, and discount factors. While previous work with UDRL demonstrated it in a traditional online RL setting, here we show that this single algorithm can also work in the imitation learning and offline RL settings, be extended to the goal-conditioned RL setting, and even the meta-RL setting. With a general agent architecture, a single UDRL agent can learn across all paradigms.

Machine learning has successfully framed many sequential decision making problems as either supervised prediction, or optimal decision-making policy identification via reinforcement learning. In data-constrained offline settings, both approaches may fail as they assume fully optimal behavior or rely on exploring alternatives that may not exist. We introduce an inherently different approach that identifies possible "dead-ends" of a state space. We focus on the condition of patients in the intensive care unit, where a "medical dead-end" indicates that a patient will expire, regardless of all potential future treatment sequences. We postulate "treatment security" as avoiding treatments with probability proportional to their chance of leading to dead-ends, present a formal proof, and frame discovery as an RL problem. We then train three independent deep neural models for automated state construction, dead-end discovery and confirmation. Our empirical results discover that dead-ends exist in real clinical data among septic patients, and further reveal gaps between secure treatments and those that were administered.

In this work, we study the simple yet universally applicable case of reward shaping in value-based Deep Reinforcement Learning (DRL). We show that reward shifting in the form of the linear transformation is equivalent to changing the initialization of the Q-function in function approximation. Based on such an equivalence, we bring the key insight that a positive reward shifting leads to conservative exploitation, while a negative reward shifting leads to curiosity-driven exploration. Accordingly, conservative exploitation improves offline RL value estimation, and optimistic value estimation improves exploration for online RL. We validate our insight on a range of RL tasks and show its improvement over baselines: (1) In offline RL, the conservative exploitation leads to improved performance based on off-the-shelf algorithms; (2) In online continuous control, multiple value functions with different shifting constants can be used to tackle the exploration-exploitation dilemma for better sample efficiency; (3) In discrete control tasks, a negative reward shifting yields an improvement over the curiosity-based exploration method.

Reinforcement Learning with Verifiable Rewards (RLVR) for large language models (LLMs) has achieved remarkable progress in enhancing LLMs' reasoning capabilities on tasks with clear correctness criteria, such as mathematical reasoning tasks. Several training metrics, such as entropy or response length, have been observed to correlate with different reasoning behaviors in reinforcement learning. Prior approaches incorporate such priors through reward or advantage shaping, which often relies on hand-crafted penalties and preferences (e.g., higher-is-better or lower-is-better). However, without careful hyperparameter tuning, these directional priors can be overly biased and may lead to failure. To this end, we introduce Conditional advANtage estimatiON (CANON), amplifying the impact of the target metric without presuming its direction. Specifically, CANON regroups the sampled responses into two groups based on the higher or lower value of a target metric, measures which metric trend contributes to better performance through inter-group comparison, and identifies the better response within the same group. In summary, CANON based on entropy consistently outperforms prior methods across three LLMs on both math reasoning and high-complexity logic tasks. When applied to response length, CANON further improves token efficiency, yielding a more favorable Pareto frontier in the performance-cost trade-off.

Although large visual-language models (LVLMs) have demonstrated strong performance in multimodal tasks, errors may occasionally arise due to biases during the reasoning process. Recently, reward models (RMs) have become increasingly pivotal in the reasoning process. Specifically, process RMs evaluate each reasoning step, outcome RMs focus on the assessment of reasoning results, and critique RMs perform error analysis on the entire reasoning process, followed by corrections. However, existing benchmarks for vision-language RMs (VLRMs) typically assess only a single aspect of their capabilities (e.g., distinguishing between two answers), thus limiting the all-round evaluation and restricting the development of RMs in the visual-language domain. To address this gap, we propose a comprehensive and challenging benchmark, dubbed as VLRMBench, encompassing 12,634 questions. VLRMBench is constructed based on three distinct types of datasets, covering mathematical reasoning, hallucination understanding, and multi-image understanding. We design 12 tasks across three major categories, focusing on evaluating VLRMs in the aspects of process understanding, outcome judgment, and critique generation. Extensive experiments are conducted on 21 open-source models and 5 advanced closed-source models, highlighting the challenges posed by VLRMBench. For instance, in the `Forecasting Future', a binary classification task, the advanced GPT-4o achieves only a 76.0% accuracy. Additionally, we perform comprehensive analytical studies, offering valuable insights for the future development of VLRMs. We anticipate that VLRMBench will serve as a pivotal benchmark in advancing VLRMs. Code and datasets will be available at https://github.com/JCruan519/VLRMBench.

Offline reinforcement learning (RL) optimizes the policy on a previously collected dataset without any interactions with the environment, yet usually suffers from the distributional shift problem. To mitigate this issue, a typical solution is to impose a policy constraint on a policy improvement objective. However, existing methods generally adopt a ``one-size-fits-all'' practice, i.e., keeping only a single improvement-constraint balance for all the samples in a mini-batch or even the entire offline dataset. In this work, we argue that different samples should be treated with different policy constraint intensities. Based on this idea, a novel plug-in approach named Guided Offline RL (GORL) is proposed. GORL employs a guiding network, along with only a few expert demonstrations, to adaptively determine the relative importance of the policy improvement and policy constraint for every sample. We theoretically prove that the guidance provided by our method is rational and near-optimal. Extensive experiments on various environments suggest that GORL can be easily installed on most offline RL algorithms with statistically significant performance improvements.

RL with Verifiable Rewards (RLVR) has emerged as a promising paradigm for improving the reasoning abilities of large language models (LLMs). Current methods rely primarily on policy optimization frameworks like PPO and GRPO, which follow generalized policy iteration that alternates between evaluating the current policy's value and improving the policy based on evaluation. While effective, they often suffer from training instability and diversity collapse, requiring complex heuristic tricks and careful tuning. We observe that standard RLVR in math reasoning can be formalized as a specialized finite-horizon Markov Decision Process with deterministic state transitions, tree-structured dynamics, and binary terminal rewards. Though large in scale, the underlying structure is simpler than general-purpose control settings for which popular RL algorithms (e.g., PPO) were developed, suggesting that several sophisticated techniques in existing methods may be reduced or even omitted. Based on this insight, we prove a surprising result: the optimal action can be recovered from the Q-function of a fixed uniformly random policy, thereby bypassing the generalized policy iteration loop and its associated heuristics. We introduce Random Policy Valuation for Diverse Reasoning (ROVER) to translate this principle into a practical and scalable algorithm for LLM math reasoning, a minimalist yet highly effective RL method that samples actions from a softmax over these uniform-policy Q-values. ROVER preserves diversity throughout training, allowing sustained exploration of multiple valid pathways. Across multiple base models and standard math reasoning benchmarks, ROVER demonstrates superior performance in both quality (+8.2 on pass@1, +16.8 on pass@256) and diversity (+17.6\%), despite its radical simplification compared to strong, complicated existing methods.

Reward finetuning has emerged as a promising approach to aligning foundation models with downstream objectives. Remarkable success has been achieved in the language domain by using reinforcement learning (RL) to maximize rewards that reflect human preference. However, in the vision domain, existing RL-based reward finetuning methods are limited by their instability in large-scale training, rendering them incapable of generalizing to complex, unseen prompts. In this paper, we propose Proximal Reward Difference Prediction (PRDP), enabling stable black-box reward finetuning for diffusion models for the first time on large-scale prompt datasets with over 100K prompts. Our key innovation is the Reward Difference Prediction (RDP) objective that has the same optimal solution as the RL objective while enjoying better training stability. Specifically, the RDP objective is a supervised regression objective that tasks the diffusion model with predicting the reward difference of generated image pairs from their denoising trajectories. We theoretically prove that the diffusion model that obtains perfect reward difference prediction is exactly the maximizer of the RL objective. We further develop an online algorithm with proximal updates to stably optimize the RDP objective. In experiments, we demonstrate that PRDP can match the reward maximization ability of well-established RL-based methods in small-scale training. Furthermore, through large-scale training on text prompts from the Human Preference Dataset v2 and the Pick-a-Pic v1 dataset, PRDP achieves superior generation quality on a diverse set of complex, unseen prompts whereas RL-based methods completely fail.

In this work, we investigate the synergy between supervised fine-tuning (SFT) and reinforcement learning (RL) in developing strong reasoning models. We begin by curating the SFT training data through two scaling strategies: increasing the number of collected prompts and the number of generated responses per prompt. Both approaches yield notable improvements in reasoning performance, with scaling the number of prompts resulting in more substantial gains. We then explore the following questions regarding the synergy between SFT and RL: (i) Does a stronger SFT model consistently lead to better final performance after large-scale RL training? (ii) How can we determine an appropriate sampling temperature during RL training to effectively balance exploration and exploitation for a given SFT initialization? Our findings suggest that (i) holds true, provided effective RL training is conducted, particularly when the sampling temperature is carefully chosen to maintain the temperature-adjusted entropy around 0.3, a setting that strikes a good balance between exploration and exploitation. Notably, the performance gap between initial SFT models narrows significantly throughout the RL process. Leveraging a strong SFT foundation and insights into the synergistic interplay between SFT and RL, our AceReason-Nemotron-1.1 7B model significantly outperforms AceReason-Nemotron-1.0 and achieves new state-of-the-art performance among Qwen2.5-7B-based reasoning models on challenging math and code benchmarks, thereby demonstrating the effectiveness of our post-training recipe. We release the model and data at: https://huggingface.co/nvidia/AceReason-Nemotron-1.1-7B

Training reasoning language models (LMs) with reinforcement learning (RL) for one-hot correctness inherently relies on the LM being able to explore and solve its task with some chance at initialization. Furthermore, a key use case of reasoning LMs is to act as teachers for distilling new students and cold-starting future RL iterations rather than being deployed themselves. From these considerations, we introduce a new framework that avoids RL's exploration challenge by training a new class of Reinforcement-Learned Teachers (RLTs) focused on yielding the most effective downstream distillation. RLTs are prompted with both the question and solution to each problem, and tasked to simply "connect-the-dots" with detailed explanations tailored for their students. We train RLTs with dense rewards obtained by feeding each explanation to the student and testing its understanding of the problem's solution. In practice, the raw outputs of a 7B RLT provide higher final performance on competition and graduate-level tasks than existing distillation and cold-starting pipelines that collect and postprocess the reasoning traces of orders of magnitude larger LMs. Furthermore, RLTs maintain their effectiveness when training larger students and when applied zero-shot to out-of-distribution tasks, unlocking new levels of efficiency and re-usability for the RL reasoning framework.

In reinforcement learning (RL), there are two major settings for interacting with the environment: online and offline. Online methods explore the environment at significant time cost, and offline methods efficiently obtain reward signals by sacrificing exploration capability. We propose semi-offline RL, a novel paradigm that smoothly transits from offline to online settings, balances exploration capability and training cost, and provides a theoretical foundation for comparing different RL settings. Based on the semi-offline formulation, we present the RL setting that is optimal in terms of optimization cost, asymptotic error, and overfitting error bound. Extensive experiments show that our semi-offline approach is efficient and yields comparable or often better performance compared with state-of-the-art methods.

Large language models (LLMs) trained with Reinforcement Learning from Human Feedback (RLHF) have demonstrated remarkable capabilities, but their underlying reward functions and decision-making processes remain opaque. This paper introduces a novel approach to interpreting LLMs by applying inverse reinforcement learning (IRL) to recover their implicit reward functions. We conduct experiments on toxicity-aligned LLMs of varying sizes, extracting reward models that achieve up to 80.40% accuracy in predicting human preferences. Our analysis reveals key insights into the non-identifiability of reward functions, the relationship between model size and interpretability, and potential pitfalls in the RLHF process. We demonstrate that IRL-derived reward models can be used to fine-tune new LLMs, resulting in comparable or improved performance on toxicity benchmarks. This work provides a new lens for understanding and improving LLM alignment, with implications for the responsible development and deployment of these powerful systems.

Large Language Models (LLMs) have revolutionized natural language processing, yet aligning these models with human values and preferences using RLHF remains a significant challenge. This challenge is characterized by various instabilities, such as reward hacking and catastrophic forgetting. In this technical report, we propose two innovations to stabilize RLHF training: 1) Advantage Model, which directly models advantage score i.e., extra reward compared to the expected rewards and regulates score distributions across tasks to prevent reward hacking. 2) Selective Rehearsal, which mitigates catastrophic forgetting by strategically selecting data for PPO training and knowledge rehearsing. Our experimental analysis on public and proprietary datasets reveals that the proposed methods not only increase stability in RLHF training but also achieve higher reward scores and win rates.

We introduce VisualPRM, an advanced multimodal Process Reward Model (PRM) with 8B parameters, which improves the reasoning abilities of existing Multimodal Large Language Models (MLLMs) across different model scales and families with Best-of-N (BoN) evaluation strategies. Specifically, our model improves the reasoning performance of three types of MLLMs and four different model scales. Even when applied to the highly capable InternVL2.5-78B, it achieves a 5.9-point improvement across seven multimodal reasoning benchmarks. Experimental results show that our model exhibits superior performance compared to Outcome Reward Models and Self-Consistency during BoN evaluation. To facilitate the training of multimodal PRMs, we construct a multimodal process supervision dataset VisualPRM400K using an automated data pipeline. For the evaluation of multimodal PRMs, we propose VisualProcessBench, a benchmark with human-annotated step-wise correctness labels, to measure the abilities of PRMs to detect erroneous steps in multimodal reasoning tasks. We hope that our work can inspire more future research and contribute to the development of MLLMs. Our model, data, and benchmark are released in https://internvl.github.io/blog/2025-03-13-VisualPRM/.

To obtain a near-optimal policy with fewer interactions in Reinforcement Learning (RL), a promising approach involves the combination of offline RL, which enhances sample efficiency by leveraging offline datasets, and online RL, which explores informative transitions by interacting with the environment. Offline-to-Online (O2O) RL provides a paradigm for improving an offline trained agent within limited online interactions. However, due to the significant distribution shift between online experiences and offline data, most offline RL algorithms suffer from performance drops and fail to achieve stable policy improvement in O2O adaptation. To address this problem, we propose the Robust Offline-to-Online (RO2O) algorithm, designed to enhance offline policies through uncertainty and smoothness, and to mitigate the performance drop in online adaptation. Specifically, RO2O incorporates Q-ensemble for uncertainty penalty and adversarial samples for policy and value smoothness, which enable RO2O to maintain a consistent learning procedure in online adaptation without requiring special changes to the learning objective. Theoretical analyses in linear MDPs demonstrate that the uncertainty and smoothness lead to a tighter optimality bound in O2O against distribution shift. Experimental results illustrate the superiority of RO2O in facilitating stable offline-to-online learning and achieving significant improvement with limited online interactions.