RL for Language Model Reasoning

RL: Reinforcement Learning

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91 papers in the last four weeks, up 176% on the four weeks before. 0.9% of all new papers.

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May 13, 2026cs.LG

Revisiting Reinforcement Learning with Verifiable Rewards from a Contrastive Perspective

Group Relative Policy Optimization (GRPO) is one of the most widely adopted RLVR algorithms for post-training large language models on reasoning tasks. We first show that GRPO admits an equivalent discriminative reformulation, in which policy optimization maximizes the expected score gap between verified positive and negative rollouts. This reformulation reveals two objective-level limitations: likelihood-misaligned surrogate scores, in which clipped ratio-based scores are optimized rather than the sequence likelihoods that govern generation, and score-insensitive credit assignment, in which rollout-level credit does not reflect the current score gaps between positive and negative rollouts. To address these limitations, we propose ConSPO, a Contrastive Sequence-level Policy Optimization method that uses length-normalized sequence log-probabilities as rollout scores and contrasts verified positive rollouts against negative distractors within the same group. ConSPO optimizes a group-wise InfoNCE-style objective to adaptively strengthen updates for poorly separated positives and high-scoring negatives, together with a curriculum-scheduled margin that preserves separation pressure as training progresses. Experiments across diverse settings show that ConSPO outperforms strong baselines on challenging reasoning benchmarks. Code will be released upon paper acceptance.

Feng Zhang, Xinhong Ma, Ziqiang Dong +5

Beijing Institute of Technology · Qwen Business Unit of Alibaba · The Chinese University of Hong Kong, Shenzhen +1

RL for Language Model Reasoning Group Relative Policy Optimization Policy Optimization Reinforcement Learning with Verifiable Rewards RL Post-Training Contrastive RL

May 13, 2026stat.ML

AIS: Adaptive Importance Sampling for Quantized RL

Reinforcement learning (RL) for large language models (LLMs) is dominated by the cost of rollout generation, which has motivated the use of low-precision rollouts (e.g., FP8) paired with a BF16 trainer to improve throughput and reduce memory pressure. This introduces a rollout-training mismatch that biases the policy gradient and can cause training to collapse outright on reasoning benchmarks. We show that the mismatch is non-stationary and acts as a double-edged sword: early in training it provides a stochastic exploration bonus, exposing the gradient to trajectories the trainer would otherwise under-sample, but the same perturbation transitions into a destabilizing source of bias as the policy concentrates. To solve this, we propose Adaptive Importance Sampling (AIS), a correction framework that adjusts the strength of its intervention on a per-batch basis. AIS combines three real-time diagnostics, namely weight reliability, divergence severity, and variance amplification, into a single mixing coefficient that interpolates between the uncorrected and fully importance-weighted gradients, suppressing the destabilizing component of the mismatch while preserving its exploratory benefit. We integrate AIS into GRPO and evaluate it on the diffusion-based LLaDA-8B-Instruct and the autoregressive Qwen3-8B and Qwen3.5-9B across mathematical reasoning and planning benchmarks. AIS matches the BF16 baseline on most tasks while retaining the 1.5 to 2.76x rollout speedup of FP8.

Jiajun Zhou, Wei Shao, Lingchao Zheng +2

Huawei · The University of Hong Kong

RL for Language Models Reinforcement Learning RL for Language Model Reasoning

May 12, 2026cs.LG

Multi-Rollout On-Policy Distillation via Peer Successes and Failures

Large language models are often post-trained with sparse verifier rewards, which indicate whether a sampled trajectory succeeds but provide limited guidance about where reasoning succeeds or fails. On-policy distillation (OPD) offers denser token-level supervision by training on student-generated trajectories, yet existing methods typically distill each rollout independently and ignore the other attempts sampled for the same prompt. We introduce Multi-Rollout On-Policy Distillation (MOPD), a peer-conditioned distillation framework that uses the student's local rollout group to construct more informative teacher signals. MOPD conditions the teacher on both successful and failed peer rollouts: successes provide positive evidence for valid reasoning patterns, while failures provide structured negative evidence about plausible mistakes to avoid. We study two peer-context constructions: positive peer imitation and contrastive success-failure conditioning. Experiments on competitive programming, mathematical reasoning, scientific question answering, and tool-use benchmarks show that MOPD consistently improves over standard on-policy baselines. Further teacher-signal analysis shows that mixed success-failure contexts better align teacher scores with verifier rewards, indicating that the gains arise from more faithful, instance-adaptive supervision. These results indicate that effective on-policy distillation should exploit the student's multi-rollout trial-and-error behavior rather than treating rollouts as isolated samples.

Weichen Yu, Xiaomin Li, Yizhou Zhao +8

1Carnegie Mellon University · 2Microsoft · 3Purdue University

RL for Language Model Reasoning Language Model Distillation Reinforcement Learning with Verifiable Rewards On-Policy Distillation Teacher-Student Learning

May 12, 2026cs.LG

Learning, Fast and Slow: Towards LLMs That Adapt Continually

Large language models (LLMs) are trained for downstream tasks by updating their parameters (e.g., via RL). However, updating parameters forces them to absorb task-specific information, which can result in catastrophic forgetting and loss of plasticity. In contrast, in-context learning with fixed LLM parameters can cheaply and rapidly adapt to task-specific requirements (e.g., prompt optimization), but cannot by itself typically match the performance gains available through updating LLM parameters. There is no good reason for restricting learning to being in-context or in-weights. Moreover, humans also likely learn at different time scales (e.g., System 1 vs 2). To this end, we introduce a fast-slow learning framework for LLMs, with model parameters as "slow" weights and optimized context as "fast" weights. These fast "weights" can learn from textual feedback to absorb the task-specific information, while allowing slow weights to stay closer to the base model and persist general reasoning behaviors. Fast-Slow Training (FST) is up to 3x more sample-efficient than only slow learning (RL) across reasoning tasks, while consistently reaching a higher performance asymptote. Moreover, FST-trained models remain closer to the base LLM (up to 70% less KL divergence), resulting in less catastrophic forgetting than RL-training. This reduced drift also preserves plasticity: after training on one task, FST trained models adapt more effectively to a subsequent task than parameter-only trained models. In continual learning scenarios, where task domains change on the fly, FST continues to acquire each new task while parameter-only RL stalls.

Rishabh Tiwari, Kusha Sareen, Lakshya A Agrawal +6

1UC Berkeley · 4Eragon · 2Mila +3

Continual Learning for LLMs RL for Language Model Reasoning In-Context Learning Catastrophic Forgetting

May 12, 2026cs.LG

Beyond GRPO and On-Policy Distillation: An Empirical Sparse-to-Dense Reward Principle for Language-Model Post-Training

In settings where labeled verifiable training data is the binding constraint, each checked example should be allocated to the model and reward density where it is most informative. We identify a reward-density principle that governs this allocation: sparse sequence-level reward is most useful on models that can explore and discover better behavior, while dense token-level teacher supervision is better suited for compressing that behavior into a smaller deployment model. The principle yields a simple allocation rule: use scarce labeled data upstream on the strongest available teacher, then transfer the reward-shaped behavior downstream as dense supervision. We evaluate this rule through a four-stage workflow -- teacher RL, forward-KL warmup, on-policy distillation, optional post-bridge student RL -- on verifiable math with Qwen3 and Llama models. At fixed Qwen3-1.7B deployment-student size, an RL-improved 8B teacher distilled through the dense bridge outperforms direct GRPO on the same student (

79.3\%

vs.\

75.9\%

on MATH;

25.2\%

vs.\

19.8\%

on AIME~2024, avg@16), while transfer from the same teacher \emph{before} RL underperforms. A component ablation confirms that each stage is load-bearing: replacing the RL-improved teacher with a raw teacher costs

7.8

MATH points, removing the forward-KL warmup costs

1.7

, and removing on-policy distillation costs

3.3

. The teacher-quality ordering -- raw-teacher transfer

<

direct GRPO

<

RL-teacher transfer -- replicates on Llama-3.1-8B-Instruct with a Llama-3.3-70B-Instruct teacher. The operational lesson is to avoid spending scarce labeled data on the least prepared policy: use sparse reward for teacher-side discovery, dense transfer for student compression, and student-side sparse reward only after the bridge.

Yuanda Xu, Hejian Sang, Zhengze Zhou +3

Reinforcement Learning RL for Language Model Reasoning Language Model Distillation On-Policy Distillation Sparse-Reward RL Teacher-Student Learning

May 12, 2026cs.LG

Holder Policy Optimisation

Group Relative Policy Optimisation (GRPO) enhances large language models by estimating advantages across a group of sampled trajectories. However, mapping these trajectory-level advantages to policy updates requires aggregating token-level probabilities within each sequence. Relying on a fixed aggregation mechanism for this step fundamentally limits the algorithm's adaptability. Empirically, we observe a critical trade-off: certain fixed aggregations frequently suffer from training collapse, while others fail to yield satisfactory performance. To resolve this, we propose \textbf{HölderPO}, a generalised policy optimisation framework unifying token-level probability aggregation via the Hölder mean. By explicitly modulating the parameter

p

, our framework provides continuous control over the trade-off between gradient concentration and variance bounds. Theoretically, we prove that a larger

p

concentrates the gradient to amplify sparse learning signals, whereas a smaller

p

strictly bounds gradient variance. Because no static configuration can universally resolve this concentration-stability trade-off, we instantiate the framework with a dynamic annealing algorithm that progressively schedules

p

across the training lifecycle. Extensive evaluations demonstrate superior stability and convergence over existing baselines. Specifically, our approach achieves a state-of-the-art average accuracy of

54.9\%

across multiple mathematical benchmarks, yielding a substantial

7.2\%

relative gain over standard GRPO and secures an exceptional

93.8\%

success rate on ALFWorld.

Yuxiang Chen, Dingli Liang, Yihang Chen +8

University College London, London, United Kingdom. · 3The Hong Kong University of Science and Technology (Guangzhou), Guangzhou, China. · 2Shanghai Jiao Tong University, Shanghai, China.

RL for Language Model Reasoning Group Relative Policy Optimization Policy Optimization

May 12, 2026cs.SE

StepCodeReasoner: Aligning Code Reasoning with Stepwise Execution Traces via Reinforcement Learning

Existing code reasoning methods primarily supervise final code outputs, ignoring intermediate states, often leading to reward hacking where correct answers are obtained through inconsistent reasoning. We propose StepCodeReasoner, a framework that introduces explicit intermediate execution-state supervision. By automatically inserting structured print-based execution-trace anchors into code, the model is trained to predict runtime states at each step, transforming code reasoning into a verifiable, stepwise execution modeling problem. Building on this execution-aware method, we introduce Bi-Level GRPO, a reinforcement learning algorithm for structured credit assignment at two levels: inter-trajectory, comparing alternative execution paths, and intra-trajectory, rewarding intermediate accuracy based on its impact on downstream correctness. Extensive experiments demonstrate that StepCodeReasoner achieves SOTA performance in code reasoning. In particular, our 7B model achieves 91.1% on CRUXEval and 86.5% on LiveCodeBench, outperforming the CodeReasoner-7B baseline (86.0% and 77.7%) and GPT-4o (85.6% and 75.1%). Furthermore, on the execution-trace benchmark REval, our model scores 82.9%, outperforming baseline CodeReasoner-7B (72.3%), its 14B counterpart (81.1%), and GPT-4o (77.3%). Additionally, our approach also improves code generation performance, demonstrating that explicit execution modeling enhances both code reasoning and code generation.

Hao Wang, Rui Li, Lei Sha +1

Beihang University, Beijing, China · Peking University, Beijing, China · Zhongguancun Laboratory, Beijing, China +1

RL for Language Model Reasoning Execution-Guided Code Generation Reinforcement Learning with Verifiable Rewards Step-Level Credit Assignment

May 12, 2026cs.LG

GEAR: Granularity-Adaptive Advantage Reweighting for LLM Agents via Self-Distillation

Reinforcement learning has become a widely used post-training approach for LLM agents, where training commonly relies on outcome-level rewards that provide only coarse supervision. While finer-grained credit assignment is promising for effective policy updates, obtaining reliable local credit and assigning it to the right parts of the long-horizon trajectory remains an open challenge. In this paper, we propose Granularity-adaptivE Advantage Reweighting (GEAR), an adaptive-granularity credit assignment framework that reshapes the trajectory-level GRPO advantage using token- and segment-level signals derived from self-distillation. GEAR compares an on-policy student with a ground-truth-conditioned teacher to obtain a reference-guided divergence signal for identifying adaptive segment boundaries and modulating local advantage weights. This divergence often spikes at the onset of a semantic deviation, while later tokens in the same autoregressive continuation may return to low divergence. GEAR therefore treats such spikes as anchors for adaptive credit regions: where the student remains aligned with the teacher, token-level resolution is preserved; where it departs, GEAR groups the corresponding continuation into an adaptive segment and uses the divergence at the departure point to modulate the segment' s advantage. Experiments across eight mathematical reasoning and agentic tool-use benchmarks with Qwen3 4B and 8B models show that GEAR consistently outperforms standard GRPO, self-distillation-only baselines, and token- or turn-level credit-assignment methods. The gains are especially strong on benchmarks with lower GRPO baseline accuracy, reaching up to around 20% over GRPO, suggesting that the proposed adaptive reweighting scheme is especially useful in more challenging long-horizon settings.

Sijia Li, Yuchen Huang, Zifan Liu +7

Hong Kong University of Science and Technology · Microsoft Research Asia

RL for Language Model Reasoning Credit Assignment in RL Policy Learning Reward Design for RL RL for LLM Agents RL for Tool Use

May 12, 2026cs.LG

Entropy Polarity in Reinforcement Fine-Tuning: Direction, Asymmetry, and Control

Policy entropy has emerged as a fundamental measure for understanding and controlling exploration in reinforcement learning with verifiable rewards (RLVR) for LLMs. However, existing entropy-aware methods mainly regulate entropy through global objectives, while the token-level mechanism by which sampled policy updates reshape policy entropy remains underexplored. In this work, we develop a theoretical framework of entropy mechanics in RLVR. Our analysis yields a first-order approximation of the entropy change, giving rise to entropy polarity, a signed token-level quantity that predicts how much a sampled update expands or contracts entropy. This analysis further reveals a structural asymmetry: reinforcing frequent high-probability tokens triggers contraction tendencies, whereas expansive tendencies typically require lower-probability samples or stronger distributional correction. Empirically, we show that entropy polarity reliably predicts entropy changes, and that positive and negative polarity branches play complementary roles in preserving exploration while strengthening exploitation. Building on these insights, we propose Polarity-Aware Policy Optimization (PAPO), which preserves both polarity branches and implements entropy control through advantage reweighting. With the empirical entropy trajectory as an online phase signal, PAPO adaptively reallocates optimization pressure between entropy-expanding and entropy-contracting updates. Experiments on mathematical reasoning and agentic benchmarks show that PAPO consistently outperforms competitive baselines, while delivering superior training efficiency and substantial reward improvements.

Jiazheng Zhang, Ziche Fu, Junrui Shen +17

Fudan NLP Group, Honor Device Co., Ltd · University of Hong Kong, Shanghai Jiao Tong University and Tencent Hunyuan

RL for Language Model Reasoning Policy Optimization Maximum Entropy RL Reinforcement Learning with Verifiable Rewards

May 12, 2026cs.AI

Seirênes: Adversarial Self-Play with Evolving Distractions for LLM Reasoning

We present Seirênes, a self-play RL framework that transforms contextual interference from a failure mode of LLM reasoning into an internal training signal for co-evolving more resilient reasoners. While RL with verifiable rewards has significantly advanced reasoning capabilities, models can still exhibit fragility when encountering non-idealized contexts: scenarios characterized by superfluous information, tangential instructions, or incidental correlations that differ from the clean distributions typical of standard benchmarks. Seirênes harnesses this vulnerability through a parameter-shared and adversarial self-play loop. Within this framework, a single model is trained to both construct plausible yet distracting contexts that expose its own reasoning blind spots, and solve problems by discerning the essential task from these perturbations to recover the core underlying logic. By pitting these competing objectives against each other, Seirênes compels the model to move beyond superficial pattern matching and anchors its capabilities in robust underlying reasoning. This continuous interaction sustains an informative co-evolutionary curriculum as the model improves. Across seven mathematical reasoning benchmarks and model scales from 4B to 30B, Seirênes achieves average gains of +10.2, +9.1, and +7.2 points. Besides, distracting contexts produced by the 4B Seirênes model reduce the accuracy of top-tier closed-source models (GPT and Gemini) by roughly 4--5 points, revealing Seirênes' general ability to uncover reasoning models' blind spots.

Chi Zhang, Haibo Qiu, Qiming Zhang +3

School of Computer Science, Wuhan University · Meituan Inc · Independent Researchers +1

RL for Language Model Reasoning Adversarial Attacks on LLMs Mathematical Reasoning Adversarial Robustness of Language Models

May 12, 2026cs.AI

Nice Fold or Hero Call: Learning Budget-Efficient Thinking for Adaptive Reasoning

Large reasoning models (LRMs) improve problem solving through extended reasoning, but often misallocate test-time compute. Existing efficiency methods reduce cost by compressing reasoning traces or conditioning budget on perceived difficulty, yet largely overlook solvability. As a result, they may spend large budgets on queries beyond the model's capability while compressing hard-but-solvable queries that require deeper reasoning. In this work, we formulate adaptive reasoning as a computational investment under uncertainty, where budget should follow the expected return of reasoning rather than perceived difficulty alone. To instantiate this principle, we propose Budget-Efficient Thinking (BET), a two-stage framework that combines behavioral cold-start with GRPO under an investment-cost-aware reward. By aligning solve-or-fold decisions with rollout-derived solvability, BET learns three behaviors: (1) short solve, answering easy queries concisely; (2) nice fold, abstaining early when continued reasoning has near-zero expected return; and (3) hero call, preserving sufficient compute for hard-but-solvable queries. Across seven benchmarks and three base models, BET reduces reasoning tokens by ~55% on average while achieving overall performance improvements, and transfers zero-shot from mathematical reasoning to scientific QA and logical reasoning with comparable efficiency gains.

Zhaomeng Zhou, Lan Zhang, Junyang Wang +2

University of Science and Technology of China · The Chinese University of Hong Kong

RL for Language Model Reasoning Efficient Language Model Reasoning Inference-Time Compute Allocation Efficient Language Model Inference LLM Mathematical Reasoning Large Reasoning Models

May 12, 2026cs.LG

Anti-Self-Distillation for Reasoning RL via Pointwise Mutual Information

On-policy self-distillation, where a student is pulled toward a copy of itself conditioned on privileged context (e.g., a verified solution or feedback), offers a promising direction for advancing reasoning capability without a stronger external teacher. Yet in math reasoning the gains are inconsistent, even when the same approach succeeds elsewhere. A pointwise mutual information analysis traces the failure to the privileged context itself: it inflates the teacher's confidence on tokens already implied by the solution (structural connectives, verifiable claims) and deflates it on deliberation tokens ("Wait", "Let", "Maybe") that drive multi-step search. We propose Anti-Self-Distillation (AntiSD), which ascends a divergence between student and teacher rather than descending it: this reverses the per-token sign and yields a naturally bounded advantage in one step. An entropy-triggered gate disables the term once the teacher entropy collapses, completing a drop-in replacement for default self-distillation. Across five models from 4B to 30B parameters on math reasoning benchmarks, AntiSD reaches the GRPO baseline's accuracy in 2 to 10x fewer training steps and improves final accuracy by up to 11.5 points. AntiSD opens a path to scalable self-improvement, where a language model bootstraps its own reasoning through its training signal.

Guobin Shen, Xiang Cheng, Chenxiao Zhao +4

1Xiaohongshu Inc. · Institute of Automation, Chinese Academy of Sciences

On-Policy Self-Distillation RL for Language Model Reasoning Self-Distillation Teacher-Student Learning LLM Mathematical Reasoning

May 12, 2026cs.CL

Taming Extreme Tokens: Covariance-Aware GRPO with Gaussian-Kernel Advantage Reweighting

Group Relative Policy Optimization (GRPO) has emerged as a promising approach for improving the reasoning capabilities of large language models. However, it struggles to effectively balance the tradeoff between exploration and exploitation during training, often resulting in suboptimal performance. Motivated by the theoretical insight that changes in entropy are governed by the covariance between token probabilities and their corresponding advantages, we propose a hyperparameter-free, covariance-weighted optimization method that dynamically down-weights extreme token-level updates via a Gaussian kernel. This approach automatically reduces the instability caused by exploration-exploitation trade-off while preserving informative learning signals. Extensive empirical evaluations show that our approach improves downstream performance across reasoning benchmarks compared with GRPO, and effectively stablizes entropy as training progresses.

Cheng Wang, Qin Liu, Wenxuan Zhou +1

National University of Singapore · University of California, Davis · University of Southern California

Reinforcement Learning RL for Language Model Reasoning Group Relative Policy Optimization

May 12, 2026cs.AI

Selective Off-Policy Reference Tuning with Plan Guidance

Reinforcement learning with verifiable rewards helps reasoning, but GRPO-style methods stall on hard prompts where all sampled rollouts fail. SORT adds a repair update for those failures without changing rollout generation: it derives a plan from the reference solution, compares token probabilities with and without that plan, and gives higher weight to tokens that become more predictable under plan conditioning. This turns all-wrong prompts into selective, structure-aware learning signals instead of uniform imitation. Across three backbones and eight reasoning benchmarks, SORT improves over GRPO and guidance baselines, with largest gains on weaker models.

Duc Anh Le, Tien-Phat Nguyen, Thien Huu Nguyen +2

Independent Author · Hanoi University of Science and Technology, Hanoi, Vietnam · University of Oregon, Eugene, OR, USA +1

Reinforcement Learning RL for Language Model Reasoning Reinforcement Learning with Verifiable Rewards Policy Learning Off-Policy RL

May 12, 2026cs.LG

Understanding and Preventing Entropy Collapse in RLVR with On-Policy Entropy Flow Optimization

Reinforcement learning with verifiable rewards (RLVR) has become an effective paradigm for improving the reasoning ability of large language models. However, widely used RLVR algorithms, such as GRPO, often suffer from entropy collapse, leading to premature determinism and unstable optimization. Existing remedies, including entropy regularization and ratio-based clipping heuristics, either control entropy in a coarse-grained manner or rely on approximate on-policy training. In this paper, we revisit entropy collapse from a token-level entropy flow perspective. Our analysis reveals that entropy-decreasing tokens consistently outweigh entropy-increasing ones, resulting in a severely imbalanced entropy flow. This perspective provides a unified explanation of entropy collapse in existing RLVR algorithms and highlights the importance of balancing entropy dynamics. Motivated by this analysis, we propose On-Policy Entropy Flow Optimization (OPEFO), an adaptive entropy flow balancing mechanism that rescales entropy-increasing and entropy-decreasing updates according to their contributions to entropy change, while remaining strict on-policy. Experiments on six mathematical reasoning benchmarks demonstrate that OPEFO improves training stability and final performance. We will release the code and models upon publication.

Huimin Xu, Shuai Zhao, Xiaobao Wu +1

Nanyang Technological University, Singapore · Shanghai Jiao Tong University, China · 3VinUniversity, Vietnam

Reinforcement Learning RL for Language Model Reasoning Reinforcement Learning with Verifiable Rewards Entropy Regularization

May 12, 2026cs.LG

Drop the Act: Probe-Filtered RL for Faithful Chain-of-Thought Reasoning

Reasoning models post-hoc rationalize answers they have already committed to internally, producing chains of reasoning theater: deliberative-looking steps that contribute nothing to correctness. This wastes inference tokens, pollutes interpretability, and obscures what the model actually computed. We introduce ProFIL (Probe-Filtered Reinforcement Learning) to reduce theater, increase chain-of-thought faithfulness, and shrink chain length in a single, drop-in extension to Group Relative Policy Optimization (GRPO). A multi-head attention probe is trained once on the frozen base model to detect post-commitment steps from internal activations alone; during GRPO, rollouts whose probe score exceeds a threshold have their advantage zeroed. Our central finding is that a probe trained on a frozen base, with verifier-derived labels and no human annotation, provides a stable signal that suppresses theater while resisting the RL-obfuscation failure mode predicted by prior work. Across four reasoning domains (GSM8K, LiveCodeBench, ToolUse, MMLU-Redux) and two model architectures (Llama-8B, Qwen-7B), ProFIL reduces post-commitment theater by 11--100%, raises faithful-fraction (e.g., +24pp on LiveCodeBench under an independent Claude 3.7 Sonnet judge), and shortens chains by 4--19%, all while preserving or improving task accuracy. ProFIL also beats a matched length-penalty GRPO baseline, isolating the gain as semantic commitment-detection rather than chain compression. Probe weights, training configurations, and rollouts are released across all four domains.

Swapnil Parekh, Naman Goyal

Intuit

CoT Faithfulness Faithfulness of Language Model Explanations LLM Interpretability RL for Language Model Reasoning Group Relative Policy Optimization Reasoning Trace Analysis

May 12, 2026cs.AI

Breaking $\textit{Winner-Takes-All}$ : Cooperative Policy Optimization Improves Diverse LLM Reasoning

Reinforcement learning with verifiers (RLVR) has become a central paradigm for improving LLM reasoning, yet popular group-based optimization algorithms like GRPO often suffer from exploration collapse, where the models prematurely converge on a narrow set of high-scoring patterns, lacking the ability to explore new solutions. Recent efforts attempt to alleviate this by adding entropy regularization or diversity bonus. However, these approaches do not change the \textit{winner-takes-all} nature, where rollouts still compete for individual advantage rather than cooperating for maximizing global diversity. In this work, we propose Group Cooperative Policy Optimization (GCPO), which shifts the training paradigm from rollout competition to team cooperation. Specifically, GCPO replaces independent rollout scoring with team-level credit assignment: a rollout is rewarded by how much it contributes to the team's valid solution coverage, rather than its individual accuracy. This coverage is described as a determinant volume over reward-weighted semantic embeddings, where only correct and non-redundant rollouts contribute to this volume. During advantage estimation, GCPO redistributes the collective team reward to each single rollout according to its average marginal contribution to the team. This cooperative training paradigm routes optimization toward non-redundant correct reasoning paths. Experiments across multiple reasoning benchmarks demonstrate that GCPO significantly improves both reasoning accuracy and solution diversity over existing approaches. Code will be released at https://github.com/bradybuddiemarch/gcpo.

Haoxuan Chen, Tianming Liang, Wei-Shi Zheng +1

1ISEE Lab, Sun Yat-sen University

Reinforcement Learning RL for Language Model Reasoning Policy Optimization Reinforcement Learning with Verifiable Rewards

May 12, 2026cs.AI

Adaptive Teacher Exposure for Self-Distillation in LLM Reasoning

On-policy self-distillation has become a strong recipe for LLM reasoning, where a privileged teacher supervises the student's own rollouts while conditioning on the reference solution. A design choice shared by nearly all such methods, however, has gone unquestioned: the teacher always sees the full reference reasoning. We argue that this default itself is part of the problem and identify a teacher-side exposure mismatch: when the teacher conditions on reasoning far beyond the student's current competence, the resulting token targets become too strong to absorb. A controlled fixed-exposure sweep makes this concrete on two fronts: 1) full exposure is not reliably the best choice, and 2) student-teacher mismatch grows monotonically as the teacher sees more privileged reasoning. This motivates treating teacher exposure not as a fixed hyperparameter but as a learnable training-time control variable. We therefore propose Adaptive Teacher Exposure for Self-Distillation (ATESD). ATESD models the reveal ratio with a lightweight Beta-policy controller conditioned on compact training-state statistics, and uses one sampled exposure for a short hold window of student updates. To make this exposure controller learnable, we optimize it with a discounted learning-progress reward that scores each held decision by its effect on the student's future improvement rather than its immediate loss change, addressing the delayed credit assignment induced by on-policy distillation. Experiments on AIME 24, AIME 25, and HMMT 25 across Qwen3-{1.7B, 4B, 8B} show that ATESD consistently outperforms competitive self-distillation and RL baselines, improving over OPSD by +0.95, +2.05, and +2.33 Average@12 points respectively, and establishing adaptive teacher exposure as an effective new axis for reasoning self-distillation.

Zihao Han, Tiangang Zhang, Huaibin Wang +1

ByteDance Douyin

On-Policy Self-Distillation RL for Language Model Reasoning Language Model Distillation Teacher-Student Learning Knowledge Distillation

May 12, 2026cs.LG

fg-expo: Frontier-guided exploration-prioritized policy optimization via adaptive kl and gaussian curriculum

Reinforcement Learning with Verifiable Rewards (RLVR) has become the standard paradigm for LLM mathematical reasoning, with Group Relative Policy Optimization (GRPO) serving as the dominant algorithm. We identify two overlooked inefficiencies inherent in GRPO. First, a fixed KL coefficient overly restricts policy exploration at moments when the model needs to diverge significantly from the reference policy. Second, uniform question sampling overlooks that moderately difficult problems produce the most informative gradient signals. We propose FG-ExPO, short for Frontier-Guided Exploration-Prioritized Policy Optimization, which integrates two lightweight components. Accuracy-Conditioned KL Scaling (AKL) adjusts the KL penalty strength through a smooth nonlinear function of batch average accuracy, loosening the constraint when the model performs poorly and strengthening it when the model achieves satisfactory results. Gaussian Curriculum Sampling (GCS) assigns sampling weights to questions following a Gaussian distribution centered at a moderate accuracy level around 0.5, focusing model training on its learning frontier. We conduct evaluations on DeepSeek-R1-Distill-Qwen-1.5B and Qwen3-8B-Base across six mainstream mathematical reasoning benchmarks. Experimental results demonstrate that FG-ExPO consistently outperforms vanilla GRPO. It delivers an absolute improvement of 13.34 on the AIME 2025 pass@32 metric, rising from 63.33 percent to 76.67 percent, and obtains an average pass@32 gain of 2.66 on the 8B model. The substantially larger performance gains observed on pass@32 compared to pass@1 verify that FG-ExPO enlarges the model's effective exploration space under a fixed inference budget.

Mingxiong Lin, Zhangquan Gong, Maowen Tang +6

OPPO AI Center

Reinforcement Learning RL for Language Model Reasoning Curriculum RL Mathematical Reasoning RL Exploration Reinforcement Learning with Verifiable Rewards

May 11, 2026cs.LG

Internalizing Curriculum Judgment for LLM Reinforcement Fine-Tuning

In LLM Reinforcement Fine-Tuning (RFT), curriculum learning drives both efficiency and performance. Yet, current methods externalize curriculum judgment via handcrafted heuristics or auxiliary models, risking misalignment with the policy's training dynamics. In this paper, we introduce METIS (METacognitive Internalized Self-judgment), a novel framework that internalizes curriculum judgment as a native capability. Leveraging a critical observation that within-prompt reward variance effectively gauges prompt informativeness, METIS predicts this metric based on recent training outcomes as lightweight in-context learning examples. This intrinsic self-judgment then dynamically dictates the training allocation. Moreover, METIS closes the loop between judgment and optimization by jointly optimizing the standard RFT rewards and a self-judgment reward. This allows the policy to learn what to learn next, as a form of metacognition. Across mathematical reasoning, code generation, and agentic function-calling benchmarks, METIS delivers superior performance while achieving up to a 2.1x training speedup, with controlled ablations and in-depth analysis further validating the benefits of internalized curriculum judgment. By bypassing handcrafted heuristics and auxiliary models, our work establishes a simple, closed-loop, and highly efficient curriculum internalization paradigm for LLM reinforcement fine-tuning.

Han Zheng, Yining Ma, Karthick Gunasekaran +4

MIT · Amazon AGI

Reinforcement Learning Meta-Learning RL for Language Model Reasoning Curriculum RL RL Fine-Tuning

May 11, 2026cs.LG

Rebellious Student: Reversing Teacher Signals for Reasoning Exploration with Self-Distilled RLVR

Self-distillation has emerged as a powerful framework for post-training LLMs, where a teacher conditioned on extra information guides a student without it, both from the same model. While this guidance is useful when the student has failed, on successful rollouts, the same mechanism instead overwrites the student's choices and suppresses it's own reasoning. Therefore, we propose reading the original self-distillation signal in reverse: when the student succeeds along a path the teacher would not have predicted, these tokens reflect its self-driven reasoning. Building on this, we propose RLRT (RLVR with Reversed Teacher), which augments GRPO by reinforcing these tokens on correct rollouts. We interpret this as a new form of exploration in RLVR: not uniform diversity, but valuable exploration grounded in the student's own success. Across base, instruction-tuned, and thinking-tuned Qwen3 checkpoints, RLRT substantially outperforms self-distillation and exploration-based baselines, establishing information asymmetry as a new, principled design axis for RLVR.

Jeonghye Kim, Jiwon Jeon, Dongsheng Li +1

Microsoft Research · KAIST

RL for Language Model Reasoning Language Model Distillation Reinforcement Learning with Verifiable Rewards Self-Distillation Teacher-Student Learning

May 11, 2026cs.LG

Equilibrium Residuals Expose Three Regimes of Matrix-Game Strategic Reasoning in Language Models

Large language models can score well on named game-theory benchmarks while failing on the same strategic computation once semantic cues are removed. We show this gap with procedurally generated zero-sum matrix games: a model that recognizes familiar games drops to 34%, 18%, and 2% success on anonymous

2{\times}2

,

3{\times}3

, and

5{\times}5

payoff matrices. The benchmark separates semantic recall, learned approximate Nash computation, and an output-interface bottleneck that limits scale. Training only on

2{\times}2

and

3{\times}3

games, supervised fine-tuning raises unseen

5{\times}5

--

7{\times}7

success from 2% to 61%, while exploitability-reward training averages 37% with high seed variance. We prove that the exploitability residual is

2

-Lipschitz in payoff perturbations, unlike discontinuous vertex-returning LP equilibrium selectors, explaining why residual training can transfer under payoff shifts even when formatting instability limits mean performance. A dominated-action padding experiment provides causal evidence: trained models solve

3{\times}3

games embedded in much larger matrices, while random-padded controls fail and dense

12{\times}12

games remain near failure. Procedural evaluation is therefore necessary for measuring strategic reasoning, and residual rewards expose a real but format-limited route to approximate equilibrium computation.

Wenhua Nie, Binhan Luo, Zijie Meng +2

National Taiwan University

Nash Equilibrium LLM Evaluation Game Theory RL for Language Model Reasoning Zero-Sum Games Nash Equilibrium Computation

May 11, 2026cs.AI

TMAS: Scaling Test-Time Compute via Multi-Agent Synergy

Test-time scaling has become an effective paradigm for improving the reasoning ability of large language models by allocating additional computation during inference. Recent structured approaches have further advanced this paradigm by organizing inference across multiple trajectories, refinement rounds, and verification-based feedback. However, existing structured test-time scaling methods either weakly coordinate parallel reasoning trajectories or rely on noisy historical information without explicitly deciding what should be retained and reused, limiting their ability to balance exploration and exploitation. In this work, we propose TMAS, a framework for scaling test-time compute via multi-agent synergy. TMAS organizes inference as a collaborative process among specialized agents, enabling structured information flow across agents, trajectories, and refinement iterations. To support effective cross-trajectory collaboration, TMAS introduces hierarchical memories: the experience bank reuses low-level reliable intermediate conclusions and local feedback, while the guideline bank records previously explored high-level strategies to steer subsequent rollouts away from redundant reasoning patterns. Furthermore, we design a hybrid reward reinforcement learning scheme tailored to TMAS, which jointly preserves basic reasoning capability, enhances experience utilization, and encourages exploration beyond previously attempted solution strategies. Extensive experiments on challenging reasoning benchmarks show that TMAS achieves stronger iterative scaling than existing test-time scaling baselines, with hybrid reward training further improving scaling effectiveness and stability across iterations. Code and data are available at https://github.com/IQuestLab/tmas.

George Wu, Nan Jing, Qing Yi +7

1IQuest Research · 2Beihang University

Multi-Agent LLM Systems RL for Language Model Reasoning Test-Time Scaling Memory-Augmented Language Model Agents

May 11, 2026cs.LG

ReCrit: Transition-Aware Reinforcement Learning for Scientific Critic Reasoning

Large language models can fail in critic interaction not only by answering incorrectly, but also by abandoning an initially correct scientific solution after user criticism. This is especially risky in scientific reasoning, where user criticism can turn a valid answer into an incorrect one. We frame critic interaction as an inter-turn correctness-transition problem rather than a final-answer accuracy problem, and identify three challenges: transition awareness, decoupling useful correction from harmful sycophancy, and scalable rollout. We propose ReCrit, a transition-aware reinforcement learning framework that decomposes Initial-to-Critic behavior into four quadrants: Correction, Sycophancy, Robustness, and Boundary. ReCrit rewards correction and robustness, penalizes sycophancy, and treats persistent errors as weak boundary signals. To make interaction training practical, ReCrit further uses dynamic asynchronous rollout with tail-adaptive completion to reduce rollout waiting. On three scientific reasoning benchmarks, ChemBench, TRQA, and EarthSE, ReCrit improves average Critic accuracy from 38.15 to 51.49 on Qwen3.5-4B and from 45.40 to 55.59 on Qwen3.5-9B. Ablations show that final-answer rewards provide little interaction-level gain, while transition-aware rewards and quadrant weighting produce more distinguishable training signals and larger net Critic-stage improvement. The code is available at https://github.com/black-yt/ReCrit .

Wanghan Xu, Yuhao Zhou, Hengyuan Zhao +8

Shanghai Jiao Tong University · Shanghai Artificial Intelligence Laboratory · This work was done during his internship at Shanghai Artificial Intelligence Laboratory. +4

LLM Sycophancy Scientific Reasoning RL for Language Model Reasoning

May 11, 2026cs.CL

Relative Score Policy Optimization for Diffusion Language Models

Diffusion large language models (dLLMs) offer a promising route to parallel and efficient text generation, but improving their reasoning ability requires effective post-training. Reinforcement learning with verifiable rewards (RLVR) is a natural choice for this purpose, yet its application to dLLMs is hindered by the absence of tractable sequence-level log-ratios, which are central to standard policy optimization. The lack of tractable sequence-level log-ratios forces existing methods to rely on high-variance ELBO-based approximations, where high verifier rewards can amplify inaccurate score estimates and destabilize RL training. To overcome this issue, we propose \textbf{R}elative \textbf{S}core \textbf{P}olicy \textbf{O}ptimization (RSPO), a simple RLVR method that uses verifiable rewards to calibrate noisy likelihood estimates in dLLMs. The core of our algorithm relies on a key observation: a reward advantage can be interpreted not only as an update direction, but also as a target for the relative log-ratio between the current and reference policies. Accordingly, RSPO calibrates this noisy relative log-ratio estimate by comparing its reward advantage with the reward-implied target relative log-ratio, updating the policy according to the gap between the current estimate and the target rather than the raw advantage alone. Experiments on mathematical reasoning and planning benchmarks show that RSPO yields especially strong gains on planning tasks and competitive mathematical-reasoning performance.

Zichao Yu, Shengze Xu, Bingqing Jiang +2

University of Science and Technology of China · The Chinese University of Hong Kong · The University of Hong Kong

RL for Language Model Reasoning Reinforcement Learning with Verifiable Rewards RL for Diffusion Models Diffusion Language Models

May 11, 2026cs.AI

STEPS: Selective On-Policy Self-Distillation for Reasoning

On-policy self-distillation (OPSD) uses a model as its own teacher under privileged context, providing token-level supervision on the model's own reasoning trajectories. However, persistent all-token guidance can degrade training in our math RL setting. Such guidance may unnecessarily constrain non-critical tokens and reinforce biases induced by privileged information unavailable at inference. Motivated by these risks, we propose STEPS, a selective OPSD framework that controls the location, direction, and duration of distillation. STEPS identifies critical spans in student rollouts, applies forward KL to key spans or reverse KL to error spans, and gradually transitions to pure GRPO after a short distillation phase. Across four models from three families, STEPS improves mean accuracy over GRPO. On Qwen3-8B, it raises average accuracy across four math benchmarks and GPQA-Diamond by an absolute 2.76% with a strong annotator. Using the training policy as its own annotator yields an absolute mean gain of 1.90%, with an estimated 2.7% training-time overhead amortized over 300 steps. Controlled ablations support semantic span selection, class-specific KL directions, and the hand-off to GRPO. Together, these results support brief, targeted self-distillation as an efficient complement to reward-driven reasoning training.

Jiaxuan Wang, Xuan Ouyang, Zhiyu Chen +2

State Key Laboratory of Novel Software Technology, Nanjing University · School of Intelligence Science and Technology, Nanjing University · AMAP, Alibaba Group +2

On-Policy Self-Distillation RL for Language Model Reasoning Teacher-Student Learning RL Fine-Tuning

May 11, 2026cs.AI

expo: Exploration-prioritized policy optimization via adaptive kl regulation and gaussian curriculum sampling

Reinforcement Learning with Verifiable Rewards (RLVR) has become the standard paradigm for LLM mathematical reasoning, where Group Relative Policy Optimization (GRPO) serves as the mainstream algorithm. We point out two understudied inefficiencies existing in GRPO. First, the fixed KL penalty coefficient overly restricts policy exploration at stages where the model requires significant deviation from the reference policy. Second, uniform sampling of training questions ignores that moderately difficult problems provide the most informative gradient signals for optimization. We propose Exploration-Prioritized Policy Optimization (EXPO) with two lightweight plug-in modules. The Accuracy-Conditioned KL Scaling (AKL) dynamically adjusts KL regularization strength through a smooth nonlinear function of batch average accuracy, relaxing the penalty when the model underperforms and strengthening it when the model achieves good results. The Gaussian Curriculum Sampling (GCS) assigns sampling weights to questions following a Gaussian distribution centered at moderate accuracy around 0.5, focusing training on the model's learning frontier. We conduct extensive experiments on DeepSeek-R1-Distill-Qwen-1.5B and Qwen3-8B-Base over six mathematical reasoning benchmarks. The results show EXPO steadily surpasses vanilla GRPO. It obtains an absolute gain of 13.34 on AIME 2025 pass@32, rising from 63.33 percent to 76.67 percent, and achieves an average pass@32 improvement of 2.66 on the 8B model. The much larger performance gains on pass@32 compared with pass@1 demonstrate that EXPO effectively enlarges the model's exploration boundary under a fixed inference cost budget.

Mingxiong Lin, Zhangquan Gong, Maowen Tang +6

OPPO AI Center

Reinforcement Learning KL-Regularized RL RL for Language Model Reasoning Group Relative Policy Optimization Curriculum RL RL Exploration+2

May 11, 2026cs.LG

Verifier-Free RL for LLMs via Intrinsic Gradient-Norm Reward

While Reinforcement Learning with Verifiable Rewards (RLVR) has recently emerged as a promising post-training paradigm for Large Language Models (LLMs), its dependency on the gold label or domain-specific verifiers limits its scalability to new tasks and domains. In this work, we propose Verifier-free Intrinsic Gradient-Norm Reward (VIGOR), a simple reward that uses only the policy model itself. Given a prompt, VIGOR samples a group of completions and assigns higher within-group rewards to outputs that induce smaller

\ell_2

norms of the teacher-forced negative log-likelihood gradients under the current parameters. Intuitively, lower gradient norms suggest the completion aligns better with the current policy, serving as an intrinsic preference signal for policy optimization. To make this intrinsic signal practical for RL, we correct the systematic length bias of averaged token-level gradients with a

\sqrt{T}

scaling, and apply group-wise rank shaping to stabilize reward scales across prompts. Across mathematical reasoning benchmarks, VIGOR outperforms the state-of-the-art Reinforcement Learning from Internal Feedback (RLIF) baseline, and it also exhibits cross-domain transfer to code benchmarks when trained only on math data. For instance, on Qwen2.5-7B-Base post-trained on MATH, VIGOR improves the average math accuracy by +3.31% and the average code accuracy by +1.91% over this baseline, while exhibiting more stable training dynamics. The code is available at https://github.com/ZJUSCL/VIGOR.

Xuexiang Wen, Hang Yu, Linchao Zhu +1

1Zhejiang University · 2Ant Group

Intrinsic Reward Methods Reinforcement Learning RL for Language Model Reasoning RL Post-Training

May 11, 2026cs.LG

Exploration-Driven Optimization for Test-Time Large Language Model Reasoning

Post-training techniques combined with inference-time scaling significantly enhance the reasoning and alignment capabilities of large language models (LLMs). However, a fundamental tension arises: inference-time methods benefit from diverse sampling from a relatively flattened probability distribution, whereas reinforcement learning (RL)-based post-training inherently sharpens these distributions. To address this, we propose Exploration-Driven Optimization (EDO), which extends reward-biasing style exploration objectives to iterative post-training and integrates them into standard RL objectives, encouraging greater diversity in sampled solutions while facilitating more effective inference-time computation. We incorporate EDO into iterative Direct Preference Optimization (iDPO) and Group Relative Policy Optimization (GRPO), resulting in two variants: ED-iDPO and ED-GRPO. Extensive experiments demonstrate that both ED-iDPO and ED-GRPO exhibit greater solution diversity and improved reasoning abilities, particularly when combined with test-time computation techniques like self-consistency. Across three in-distribution reasoning benchmarks, EDO achieves a 1.0-1.3% improvement over the strongest baselines, and delivers an additional 1.5% average gain on five out-of-distribution tasks. Beyond accuracy, EDO preserves model entropy and stabilizes RL training dynamics, highlighting its effectiveness in preventing over-optimization collapse. Taken together, these results establish EDO as a practical framework for balancing exploration and exploitation in LLM reasoning, especially in settings that rely on test-time scaling.

Changhao Li, Yuchen Zhuang, Chenxiao Gao +4

Georgia Institute of Technology

RL for Language Models Inference-Time Optimization RL for Language Model Reasoning RL Post-Training LLM Reasoning

May 10, 2026cs.LG

LEAD: Length-Efficient Adaptive and Dynamic Reasoning for Large Language Models

Large reasoning models, such as OpenAI o1 and DeepSeek-R1, tend to become increasingly verbose as their reasoning capabilities improve. These inflated Chain-of-Thought (CoT) trajectories often exceed what the underlying problems require, wasting compute, latency, and context budgets. While introducing length-based efficiency rewards during reinforcement learning offers a natural remedy, existing methods struggle with two fundamental challenges: the optimal balance between correctness and efficiency is non-stationary throughout training, and intrinsic reasoning budgets vary drastically across problems. Relying on static reward weights and global length constraints inevitably forces a compromise between degraded accuracy and unrealized compression. To overcome these limitations, we propose LEAD (Length-Efficient Adaptive and Dynamic reasoning), a method that replaces static heuristics with online, self-adaptive mechanisms. LEAD dynamically calibrates the correctness-efficiency trade-off at each step using a Potential-Scaled Instability, directing optimization capacity to the most informative learning signal. Furthermore, it estimates an adaptive per-problem target length online based on the model's own correct rollouts, applying a symmetric efficiency reward that penalizes both overthinking and over-compression. Evaluated on five mathematical reasoning benchmarks, LEAD achieves the highest accuracy and Accuracy-Efficiency Score among RL-trained efficient-reasoning methods while producing substantially shorter outputs than the base model.

Songtao Wei, Yi Li, Zhikai Li +7

University of Texas at Dallas · Emory University · University of Texas at Arlington +2

RL for Language Model Reasoning Efficient Language Model Reasoning Large Reasoning Models