Reinforcement Learning with Verifiable Rewards

Also known as RLVR

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Overview

This field studies how to improve language and multimodal models by rewarding outputs whose correctness or task progress can be checked, for example with unit tests, mathematical answers, formal proofs, or simulated environments. Common approaches use policy-gradient methods such as PPO and GRPO, with outcome rewards supplemented by step-level feedback, rollout exploration, or replay to improve credit assignment and data efficiency. Work spans math and coding benchmarks as well as search, GUI, and other interactive agents. A central tension is that rewards must be scalable yet faithful: imperfect or narrow verifiers can be exploited, and a correct final answer does not by itself establish sound reasoning, visual grounding, or robust generalization.

Latest papers

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692 papers137 papers in the last four weeks, up 111% on the four weeks before. 0.8% of all new papers.

Apr 2, 2026

Apriel-Reasoner: RL Post-Training for General-Purpose and Efficient Reasoning

Building general-purpose reasoning models using reinforcement learning with verifiable rewards (RLVR) across diverse domains has been widely adopted by frontier open-weight models. However, their training recipes and domain mixtures are often not disclosed. Joint optimization across domains poses significant challenges: domains vary widely in rollout length, problem difficulty, and sample efficiency. Further, models with long chain-of-thought traces increase inference cost and latency, making efficiency critical for practical deployment. We present Apriel-Reasoner, trained with a reproducible multi-domain RL post-training recipe on Apriel-Base, a 15B-parameter open-weight LLM, across five domains using public datasets: mathematics, code generation, instruction following, logical puzzles, and function calling. We introduce adaptive domain sampling that preserves target completed-rollout ratios despite heterogeneous rollout dynamics, and a difficulty-aware length penalty that, at no additional training overhead, encourages longer reasoning for difficult problems and shorter traces for easy ones. Trained with a strict 16K-token output budget, Apriel-Reasoner remains effective at a 32K output budget and improves over Apriel-Base on AIME 2025, GPQA, MMLU-Pro, and LiveCodeBench while producing 30-50% shorter reasoning traces. Among the evaluated open-weight models of similar scale, it improves the accuracy-token tradeoff using a fully public-data recipe.

Rafael Pardinas, Ehsan Kamalloo, David Vazquez +1

ServiceNow AI Research

LLM Inference EfficiencyRL for Language Model ReasoningEfficient Language Model ReasoningReinforcement Learning with Verifiable RewardsRL Post-TrainingLarge Reasoning Models
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Apr 2, 2026

ThinkTwice: Jointly Optimizing Large Language Models for Reasoning and Self-Refinement

We introduce ThinkTwice, a simple two-phase framework that jointly optimizes LLMs to solve reasoning problems and refine the answers, based on Group Relative Policy Optimization (GRPO). In each pair of training steps, ThinkTwice first optimizes the model on solving reasoning problems, then optimizes it on refining its own solutions to the same problems, using the same binary correctness reward in both phases without correctness signals or critique annotations. Across five mathematical reasoning benchmarks and two model families including Qwen3-4B and Olmo3-7B, ThinkTwice substantially improves both reasoning and refinement performance over competitive online policy optimization baselines. Specifically, on Qwen3-4B, ThinkTwice outperforms GRPO on AIME by 5 percentage points before refinement and by 11.5 points after one self-refinement step, measured by pass@4. Analysis of the training dynamics of ThinkTwice reveals an implicit rectify-then-fortify curriculum: refinement predominantly corrects errors early in training and naturally shifts toward preserving already-correct solutions as the model improves, yielding a more rectified reward signal. Our work establishes joint training of reasoning and self-refinement as a principled and effective methodology for RLVR.

Difan Jiao, Qianfeng Wen, Blair Yang +2

Department of Computer Science, University of Toronto · Coolwei AI Lab

RL for Language Model ReasoningLLM ReasoningLLM Self-RefinementReinforcement Learning with Verifiable Rewards
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Apr 1, 2026

Learning to Hint for Reinforcement Learning

Group Relative Policy Optimization (GRPO) is widely used for reinforcement learning with verifiable rewards, but it often suffers from advantage collapse: when all rollouts in a group receive the same reward, the group yields zero relative advantage and thus no learning signal. For example, if a question is too hard for the reasoner, all sampled rollouts can be incorrect and receive zero reward. Recent work addresses this issue by adding hints or auxiliary scaffolds to such hard questions so that the reasoner produces mixed outcomes and recovers a non-zero update. However, existing hints are usually fixed rather than adapted to the current reasoner, and a hint that creates learning signal under the hinted input does not necessarily improve the no-hint policy used at test time. To this end, we propose Hint Learning for Reinforcement Learning (HiLL), a framework that jointly trains a hinter policy and a reasoner policy during RL. For each hard question, the hinter generates hints online conditioned on the current reasoner's incorrect rollout, allowing hint generation to adapt to the reasoner's evolving errors. We further introduce hint reliance, which measures how strongly correct hinted trajectories depend on the hint. We derive a transferability result showing that lower hint reliance implies stronger transfer from hinted success to no-hint success, and we use this result to define a transfer-weighted reward for training the hinter. Therefore, HiLL favors hints that not only recover informative GRPO groups, but also produce signals that are more likely to improve the original no-hint policy. Experiments across multiple benchmarks show that HiLL consistently outperforms GRPO and prior hint-based baselines, demonstrating the value of adaptive and transfer-aware hint learning for RL. The code is available at https://github.com/Andree-9/HiLL.

Yu Xia, Canwen Xu, Zhewei Yao +2

University of California, San Diego · Snowflake AI Research

Reinforcement LearningRL for Language Model ReasoningReinforcement Learning with Verifiable RewardsLLM-Guided RL
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Apr 1, 2026

Learning to Model Optimization Problems from Solver Outcomes

Automating optimization modeling with LLMs is a promising path toward scalable decision intelligence, but existing approaches either rely on agentic pipelines built on closed-source LLMs with high inference latency or fine-tune smaller LLMs using costly process supervision that often overfits to a single solver API. We study how reinforcement learning from inexpensive outcome labels can improve optimization modeling and support reuse across heterogeneous solver environments. To this end, we propose Optimization Modeling from Solver Outcomes (OMSO), which uses reinforcement learning (RL) with a mathematical programming solver as a deterministic, interactive environment. Given a natural-language problem and a target solver, OMSO generates solver-specific code, executes it in a sandboxed harness, and converts execution outcomes into scalar rewards in a closed-loop generate-execute-feedback-update process. This RL formulation learns optimization modeling without process-level supervision and supports cross-solver generalization by switching the solver environment rather than reconstructing solver-specific datasets. Experiments on NL4OPT, MAMO, IndustryOR, and OptiBench across Gurobi, OR-Tools, and COPT show that OMSO matches or outperforms process-supervised SFT, supports zero-shot training-free transfer, direct RL training, and SFT-cold-started RL, and improves modeling reasoning and semantic correctness beyond solver API usage.

Runda Guan, Xiangqing Shen, Jiajun Zhang +3

School of Computer Science and Engineering, Nanjing University of Science and Technology · School of Intelligence Science and Technology, Nanjing University · Institute of Automation, Chinese Academy of Sciences

Natural Language to Optimization ModelingLearning to OptimizeLLM-Based Program SynthesisReinforcement Learning with Verifiable Rewards
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Mar 31, 2026

Learning to Generate Formally Verifiable Step-by-Step Logic Reasoning via Structured Formal Intermediaries

Large language models (LLMs) have recently demonstrated impressive performance on complex, multi-step reasoning tasks, especially when post-trained with outcome-rewarded reinforcement learning Guo et al. 2025. However, it has been observed that outcome rewards often overlook flawed intermediate steps, leading to unreliable reasoning steps even when final answers are correct. To address this unreliable reasoning, we propose PRoSFI (Process Reward over Structured Formal Intermediates), a novel reward method that enhances reasoning reliability without compromising accuracy. Instead of generating formal proofs directly, which is rarely accomplishable for a modest-sized (7B) model, the model outputs structured intermediate steps aligned with its natural language reasoning. Each step is then verified by a formal prover. Only fully validated reasoning chains receive high rewards. The integration of formal verification guides the model towards generating step-by-step machine-checkable proofs, thereby yielding more credible final answers. PRoSFI offers a simple and effective approach to training trustworthy reasoning models.

Luoxin Chen, Yichi Zhou, Huishuai Zhang

Wangxuan Institue of Computer Technology, Peking University. · ByteDance.

LLM ReasoningLLM ReliabilityReinforcement Learning with Verifiable RewardsProcess Reward Models
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Mar 30, 2026

SOLE-R1: Video-Language Reasoning as the Sole Reward for On-Robot Reinforcement Learning

Vision-language models (VLMs) have shown impressive capabilities across diverse tasks, motivating efforts to leverage these models to supervise robot learning. However, when used as evaluators in reinforcement learning (RL), today's strongest models often fail under partial observability and distribution shift, enabling policies to exploit perceptual errors rather than solve the task. We introduce SOLE-R1 (Self-Observing LEarner), a video-language reasoning model explicitly designed to serve as the sole reward signal for online RL. Given only raw video observations and a natural-language goal, SOLE-R1 performs per-timestep spatiotemporal chain-of-thought (CoT) reasoning and produces dense estimates of task progress that can be used directly as rewards. To train SOLE-R1, we develop a large-scale video trajectory and reasoning synthesis pipeline that generates temporally grounded CoT traces aligned with continuous progress supervision. This data is combined with foundational spatial and multi-frame temporal reasoning, and used to train the model with a hybrid framework that couples supervised fine-tuning with RL from verifiable rewards. Across four different simulation environments and a real-robot setting, SOLE-R1 enables zero-shot online RL from random initialization: robots learn previously unseen manipulation tasks without ground-truth rewards, success indicators, demonstrations, or task-specific tuning. SOLE-R1 succeeds on 24 unseen tasks and substantially outperforms strong vision-language rewarders, including Robometer, RoboReward, ReWiND, GPT-5, and Gemini-3-Pro, while exhibiting markedly greater robustness to reward hacking. We release all models, data, code, and demos at the anonymous page: https://philip-mit.github.io/sole-r1/

Philip Schroeder, Thomas Weng, Karl Schmeckpeper +3

MIT · RAI Institute

RL for RoboticsMultimodal Reward ModelingVideo ReasoningRobot Learning from VideoReinforcement Learning with Verifiable RewardsReward Hacking
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Mar 30, 2026

Seeing with You: Perception-Reasoning Coevolution for Multimodal Reasoning

Reinforcement learning with verifiable rewards (RLVR) has substantially enhanced the reasoning capabilities of multimodal large language models (MLLMs). However, existing RLVR approaches typically rely on outcome-driven optimization that updates both perception and reasoning using a shared reward based solely on the final answer. This shared reward blurs credit assignment, frequently improving reasoning patterns while failing to reliably enhance the accuracy of upstream visual evidence extraction. To address this perception bottleneck, we introduce PRCO (Perception-Reasoning Coevolution), a dual-role RLVR framework with a shared policy. PRCO consists of two cooperative roles: an Observer that generates an evidence caption tailored to the question and a Solver that predicts the final answer based on this caption. Crucially, PRCO employs role-specific reward signals: the Solver is optimized using verifiable outcome rewards on the final answer, while the Observer receives a utility reward derived from the Solver's downstream success. Extensive experiments across eight challenging multimodal reasoning benchmarks demonstrate that PRCO yields consistent improvements across model scales by over 7 points on average accuracy compared to the base model, outperforming prior open-source RL-tuned baselines.

Ziqi Miao, Haonan Jia, Lijun Li +4

Multimodal ReasoningMultimodal Large Language ModelsRL for VLMsReinforcement Learning with Verifiable Rewards
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Mar 30, 2026

SARL: Label-Free Reinforcement Learning by Rewarding Reasoning Topology

Reinforcement learning is critical to improving large reasoning models, but its success relies heavily on verifiable rewards (RLVR), making it hard to use in open-ended domains where correctness is ambiguous and cannot be verified. Moreover, reasoning trajectories remain largely unconstrained, and optimizing solely toward the final answer can favor early exploitation over generalization. In this work, we ask whether general reasoning ability can be improved by teaching models how to think (the structure of reasoning) rather than what to produce (the outcome of reasoning), and we extend traditional RLVR to open-ended settings. We introduce Structure-Aware Reinforcement Learning (SARL), a label-free framework that constructs per-response reasoning maps from intermediate thinking steps and rewards their reasoning topology. SARL shifts supervision from destination to path, encouraging reasoning trajectories that are both locally coherent and globally efficient. On verifiable math tasks, SARL outperforms prior label-free RL baselines and even exceeds RL methods with ground truth supervision, with average gains of +9.1% under PPO and +11.6% under GRPO across four math benchmarks, with particularly large improvements on AIME25 (+35.5% with PPO and +44.7% with GRPO). On non-verifiable open-ended tasks, SARL achieves average gains of +34.6% under PPO and +30.4% under GRPO on WildBench across five task categories, outperforming prior label-free RL methods and DPO, which relies on additional preference labels. Beyond strong performance, SARL exhibits substantially lower KL divergence and higher policy entropy, indicating more stable and exploratory training dynamics. Code and data are available at Code Link.

Yifan Wang, Bolian Li, David Cho +3

Purdue University · Texas Instruments

RL for Language Model ReasoningReinforcement LearningReinforcement Learning with Verifiable Rewards
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Mar 29, 2026

Wan-R1: Verifiable-Reinforcement Learning for Video Reasoning

Video generation models produce visually coherent content but struggle with tasks requiring spatial reasoning and multi-step planning. Reinforcement learning (RL) offers a path to improve generalization, but its effectiveness in video reasoning hinges on reward design -- a challenge that has received little systematic study. We investigate this problem by adapting Group Relative Policy Optimization (GRPO) to flow-based video models and training them on maze-solving and robotic navigation tasks. We first show that multimodal reward models fail catastrophically in this setting. To address this, we design verifiable reward functions grounded in objective task metrics. For structured game environments, we introduce a multi-component trajectory reward. For robotic navigation, we propose an embedding-level verifiable reward. Our experiments show that RL fine-tuning with verifiable rewards improves generalization. For example, on complex 3D mazes, our model improves exact match accuracy by 29.1% over the SFT baseline, and on trap-avoidance tasks by 51.4%. Our systematic reward analysis reveals that verifiable rewards are critical for stable training, while multimodal reward models could lead to degenerate solutions. These findings establish verifiable reward design as a key enabler for robust video reasoning. Code will be publicly available.

Ming Liu, Yunbei Zhang, Shilong Liu +2

Iowa State University, Ames, IA 50011, USA · Tulane University, New Orleans, LA 70118, USA · Princeton University, Princeton, NJ 08544, USA

RL for Video ReasoningVideo ReasoningReinforcement Learning with Verifiable RewardsRL for Video GenerationMultimodal Reward Modeling
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Mar 28, 2026

Bridging Visual Representation and Reinforcement Learning from Verifiable Rewards in Large Vision-Language Models

Reinforcement Learning from Verifiable Rewards (RLVR) has substantially enhanced the reasoning capabilities of large language models in abstract reasoning tasks. However, its application to Large Vision-Language Models (LVLMs) remains constrained by a structural representational bottleneck. Existing approaches generally lack explicit modeling and effective utilization of visual information, preventing visual representations from being tightly coupled with the reinforcement learning optimization process and thereby limiting further improvements in multimodal reasoning performance. To address this limitation, we propose KAWHI (Key-Region Aligned Weighted Harmonic Incentive), a plug-and-play reward reweighting mechanism that explicitly incorporates structured visual information into uniform reward policy optimization methods (e.g., GRPO and GSPO). The method adaptively localizes semantically salient regions through hierarchical geometric aggregation, identifies vision-critical attention heads via structured attribution, and performs paragraph-level credit reallocation to align spatial visual evidence with semantically decisive reasoning steps. Extensive empirical evaluations on diverse reasoning benchmarks substantiate KAWHI as a general-purpose enhancement module, consistently improving the performance of various uniform reward optimization methods. Project page: KAWHI (https://kawhiiiileo.github.io/KAWHI_PAGE/)

Yuhang Han, Yuyang Wu, Zhengbo Jiao +6

EPIC Lab, SJTU · HKUST (GZ) · Huawei

VLM ReasoningRL for VLMsLarge Vision-Language ModelsReinforcement Learning with Verifiable RewardsReward Shaping
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Mar 28, 2026

Incentivizing Temporal-Awareness in Egocentric Video Understanding Models

Multimodal large language models (MLLMs) have recently shown strong performance in visual understanding, yet they often lack temporal awareness, particularly in egocentric settings where reasoning depends on the correct ordering and evolution of events. This deficiency stems in part from training objectives that fail to explicitly reward temporal reasoning and instead rely on frame-level spatial shortcuts. To address this limitation, we propose Temporal Global Policy Optimization (TGPO), a reinforcement learning with verifiable rewards (RLVR) algorithm designed to incentivize temporal awareness in MLLMs. TGPO contrasts model outputs generated from temporally ordered versus shuffled video frames to derive calibrated, globally normalized reward signals that explicitly favor temporally coherent reasoning. Integrated with GRPO and GSPO, TGPO supports cold-start RL training and effectively suppresses spatial shortcut behaviors learned by existing MLLMs. Experiments across five egocentric video benchmarks demonstrate that TGPO consistently improves temporal grounding and causal coherence, outperforming prior RL-based video reasoning approaches. Our results suggest that TGPO offers a simple and scalable pathway toward temporally robust MLLMs for egocentric video understanding.

Zhiyang Xu, Tian Qin, Bowen Jin +4

Virginia Tech · Harvard University · UIUC +2

Egocentric Video UnderstandingRL for VLMsTemporal Video GroundingReinforcement Learning with Verifiable Rewards
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Mar 27, 2026

Beyond Where to Look: Trajectory-Guided Reinforcement Learning for Multimodal RLVR

Recent advances in Reinforcement Learning with Verifiable Rewards (RLVR) for multimodal large language models (MLLMs) have mainly focused on improving final answer correctness and strengthening visual grounding. However, a critical bottleneck remains: although models can attend to relevant visual regions, they often fail to effectively incorporate visual evidence into subsequent reasoning, leading to reasoning chains that are weakly grounded in visual facts. To address this issue, we propose Trajectory-Guided Reinforcement Learning (TGRL), which guides the policy model to integrate visual evidence into fine-grained reasoning processes using expert reasoning trajectories from stronger models. We further introduce token-level reweighting and trajectory filtering to ensure stable and effective policy optimization. Extensive experiments on multiple multimodal reasoning benchmarks demonstrate that TGRL consistently improves reasoning performance and effectively bridges the gap between visual perception and logical reasoning.

Jinda Lu, Junkang Wu, Jinghan Li +6

University of Science and Technology of China · Pecking University · Institute of Software, Chinese Academy of Sciences

RL for VLMsMultimodal ReasoningVisually Grounded ReasoningReinforcement Learning with Verifiable RewardsLLM-Guided RL
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Mar 26, 2026

MSRL: Scaling Generative Multimodal Reward Modeling via Multi-Stage Reinforcement Learning

Recent advances in multimodal reward modeling have been largely driven by a paradigm shift from discriminative to generative approaches. Building on this progress, recent studies have further employed reinforcement learning from verifiable rewards (RLVR) to enhance multimodal reward models (MRMs). Despite their success, RLVR-based training typically relies on labeled multimodal preference data, which are costly and labor-intensive to obtain, making it difficult to scale MRM training. To overcome this limitation, we propose a Multi-Stage Reinforcement Learning (MSRL) approach, which can achieve scalable RL for MRMs with limited multimodal data. MSRL replaces the conventional RLVR-based training paradigm by first learning a generalizable reward reasoning capability from large-scale textual preference data, and then progressively transferring this capability to multimodal tasks through caption-based and fully multimodal reinforcement-learning stages. Furthermore, we introduce a cross-modal knowledge distillation approach to improve preference generalization within MSRL. Extensive experiments demonstrate that MSRL effectively scales the RLVR-based training of generative MRMs and substantially improves their performance across both visual understanding and visual generation tasks (e.g., from 66.6% to 75.9% on VL-RewardBench and from 70.2% to 75.7% on GenAI-Bench), without requiring additional multimodal preference annotations. Our code is available at: https://github.com/wangclnlp/MSRL.

Chenglong Wang, Yifu Huo, Yang Gan +8

Northeastern University, Shenyang, China · ByteDance

Multimodal Reward ModelingRL for Generative ModelsReinforcement Learning with Verifiable Rewards
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Mar 26, 2026

Bridging Perception and Reasoning: Token Reweighting for RLVR in Multimodal LLMs

Extending Reinforcement Learning with Verifiable Rewards (RLVR) to multimodal large language models (MLLMs) faces a fundamental challenge: their responses inherently interleave perception-related tokens, which ground visual content, with reasoning-related tokens, which construct reasoning chains. These token types instantiate distinct yet interdependent capacities -- visual grounding and symbolic reasoning -- making isolated optimization insufficient. Through token-level empirical analysis, we demonstrate that optimizing either perception- or reasoning-only tokens consistently underperforms full optimization, underscoring their inherent coupling. To address this, we propose a plug-and-play Token-Reweighting (ToR) strategy that explicitly models this interdependence by identifying critical tokens of both types and dynamically reweighting them during RLVR training. Applied on top of existing methods (e.g., GRPO and DAPO), ToR delivers consistent performance gains across multiple multi-modal reasoning benchmarks, achieving state-of-the-art performance with both accurate visual grounding and coherent reasoning.

Jinda Lu, Junkang Wu, Jinghan Li +6

University of Science and Technology of China · Peking University · Independent Researcher

RL for VLMsVLM ReasoningMultimodal Large Language ModelsReinforcement Learning with Verifiable Rewards
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Mar 25, 2026

Prune as You Generate: Online Rollout Pruning for Faster and Better RLVR

Reinforcement Learning with Verifiable Rewards (RLVR) has significantly advanced the reasoning capabilities of Large Language Models (LLMs). However, methods such as GRPO and DAPO suffer from substantial computational cost, since they rely on sampling many rollouts for each prompt. Moreover, in RLVR the relative advantage is often sparse: many samples become nearly all-correct or all-incorrect, yielding low within-group reward variance and thus weak learning signals. In this paper, we introduce arrol (Accelerating RLVR via online Rollout Pruning), an online rollout pruning method that prunes rollouts during generation while explicitly steering the surviving ones more correctness-balanced to enhance learning signals. Specifically, arrol trains a lightweight quality head on-the-fly to predict the success probability of partial rollouts and uses it to make early pruning decisions. The learned quality head can further weigh candidates to improve inference accuracy during test-time scaling. To improve efficiency, we present a system design that prunes rollouts inside the inference engine and re-batches the remaining ones for log-probability computation and policy updates. Across GRPO and DAPO on Qwen-3 and LLaMA-3.2 models (1B-8B), arrol improves average accuracy by +2.30 to +2.99 while achieving up to 1.7x training speedup, and yielding up to +8.33 additional gains in average accuracy in test-time scaling. The code is available at https://github.com/Hsu1023/ARRoL.

Haobo Xu, Sirui Chen, Ruizhong Qiu +5

University of Illinois at Urbana-Champaign · Amazon

RL for Language Model ReasoningReinforcement Learning with Verifiable RewardsLLM Inference Acceleration
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Mar 25, 2026

Towards Effective Experiential Learning: Dual Guidance for Utilization and Internalization

Recently, reinforcement learning~(RL) has become an important approach for improving the capabilities of large language models~(LLMs). In particular, reinforcement learning from verifiable rewards~(RLVR) has emerged as a promising paradigm for reasoning tasks. However, existing RL-based training still remains only a rough approximation to human learning. Human learners leverage both external and internal experience to guide exploration and gradually internalize useful trajectories into stable knowledge. Motivated by this gap, we ask: how can LLMs better utilize and internalize experience during RLVR training? To answer this question, we propose Dual Guidance Optimization~(DGO), a unified framework that leverages external and internal experience to improve training effectiveness. Specifically, DGO first constructs an experience bank from previously explored trajectories. The policy then performs exploration under the joint guidance of the experience bank and the model's internal knowledge. The resulting trajectories are further used to refine the experience bank and optimize model parameters, forming a closed loop of experience utilization and internalization. Experiments show that DGO consistently outperforms baseline methods, suggesting that better utilization and internalization of experience lead to more effective reasoning.

Fei Bai, Zhipeng Chen, Chuan Hao +6

Gaoling School of Artificial Intelligence, Renmin University of China · IQuest Research · Beihang University

RL for Language Model ReasoningReinforcement LearningReinforcement Learning with Verifiable RewardsExperience Replay
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Mar 24, 2026

Rethinking Token-Level Policy Optimization for Multimodal Chain-of-Thought

Multimodal Chain-of-Thought (CoT) reasoning requires large vision-language models to construct reasoning trajectories that interleave perceptual grounding with multi-step inference. However, existing Reinforcement Learning with Verifiable Rewards (RLVR) methods typically optimize reasoning at a coarse granularity, treating CoT uniformly without distinguishing their varying degrees of visual grounding. In this work, we conduct a token-level analysis of multimodal reasoning trajectories and show that successful reasoning is characterized by structured token dynamics reflecting both perceptual grounding and exploratory inference. Building upon this analysis, we propose Perception-Exploration Policy Optimization (PEPO), which derives a perception prior from hidden state similarity and integrates it with token entropy through a smooth gating mechanism to produce token-level advantages. PEPO integrates seamlessly with existing RLVR frameworks such as GRPO and DAPO, requiring neither additional supervision nor auxiliary branches. Extensive experiments across diverse multimodal benchmarks demonstrate consistent and robust improvements over strong RL baselines, spanning geometry reasoning, visual grounding, visual puzzle solving, and few-shot classification, while maintaining stable training dynamics. Code: https://github.com/xzxxntxdy/PEPO

Yunheng Li, Hangyi Kuang, Hengrui Zhang +4

VCIP, School of Computer Science, Nankai University · Kuaishou Technology

VLM ReasoningMultimodal CoT ReasoningReinforcement Learning with Verifiable Rewards
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Mar 23, 2026

Sparse but Critical: A Token-Level Analysis of Distributional Shifts in RLVR Fine-Tuning of LLMs

Reinforcement learning with verifiable rewards (RLVR) has significantly improved reasoning in large language models (LLMs), yet the token-level mechanisms underlying these improvements remain unclear. We present a systematic empirical study of RLVR's distributional effects organized around three main analyses: (1) token-level characterization of distributional shifts between base and RL models, (2) the impact of token-level distributional shifts on sequence-level reasoning performance through cross-sampling interventions, and (3) fine-grained mechanics of these shifts at the token level. We find that RL fine-tuning induces highly sparse and targeted changes, with only a small fraction of token distributions exhibiting meaningful divergence between the base and RL policies. We further characterize the structure and evolution of these shifts through analyses of token entropy, positional concentration, and reallocation of probability mass. To assess the functional importance of these sparse changes, we conduct cross-sampling experiments that selectively swap token choices between the base and RL models with varying intervention budgets. We show that inserting only a small fraction of RL-sampled tokens into base generations progressively recovers RL performance gains, while injecting a similarly small number of base token choices into otherwise RL-generated sequences collapses performance to base levels, isolating a small set of token-level decisions directly responsible for RLVR's performance gains. Finally, we explore divergence-weighted variants of the advantage signal as a diagnostic intervention, finding that they can yield improvements over baselines. Together, our results shed light on the distributional changes induced by RLVR and provide a fine-grained, token-level lens for understanding RLVR fine-tuning as a targeted refinement process.

Haoming Meng, Kexin Huang, Shaohang Wei +6

Alibaba Group

RL for Language Model ReasoningRL Fine-TuningReinforcement Learning with Verifiable RewardsCausal Interventions in Language Models
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Mar 23, 2026

On the Direction of RLVR Updates for LLM Reasoning: Identification and Exploitation

Reinforcement learning with verifiable rewards (RLVR) has substantially improved the reasoning capabilities of large language models. While existing analyses identify that RLVR-induced changes are sparse, they primarily focus on the magnitude of these updates, largely overlooking their direction. In this work, we argue that the direction of updates is a more critical lens for understanding RLVR's effects, which can be captured by the signed, token-level log probability difference Δlog⁡pΔ\log p between the base and final RLVR models. Through statistical analysis and token-replacement interventions, we demonstrate that Δlog⁡pΔ\log p more effectively identifies sparse, yet reasoning-critical updates than magnitude-based metrics (\eg divergence or entropy). Building on this insight, we propose two practical applications: (1) a test-time extrapolation method that amplifies the policy along the learned Δlog⁡pΔ\log p direction to improve reasoning accuracy without further training; (2) a training-time reweighting method that focuses learning on low-probability (corresponding to higher Δlog⁡pΔ\log p) tokens, which improves reasoning performance across models and benchmarks. Our work establishes the direction of change as a key principle for analyzing and improving RLVR.

Kexin Huang, Haoming Meng, Junkang Wu +10

Alibaba Group

RL for Language Model ReasoningReinforcement Learning with Verifiable RewardsRL Post-Training
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Mar 23, 2026

P^2O: Joint Policy and Prompt Optimization

Reinforcement Learning with Verifiable Rewards (RLVR) enhances Large Language Model (LLM) reasoning but is suffer from advantage collapse: when all rollouts of a query receive identical rewards, the group variance vanishes, most damagingly on hard samples, where scaling rollout budgets yields little. We introduce Joint Policy and Prompt Optimization (P O) to mitigate this collapse by alternating continuous policy updates with discrete prompt evolution. P O mines hard samples with a success-rate threshold, evolves reasoning prompts for them with GEPA, and internalizes the elicited trajectories via context distillation, which optimizes each trajectory under the original query and thus removes inference-time prompting, with a Context Ratio Mask (CRM) filtering out extreme likelihood ratios. P O restores critical advantage signals and surpasses the GRPO baseline by up to 8.2 points in average accuracy on six held-out benchmarks across all training datasets and backbones, while also outperforming DAPO and other baselines. The gains are especially pronounced on hard benchmarks, reaching up to 16.3 points above GRPO on average across AIME24 and AIME25. Our findings expose the limits of standard exploration in sparse-reward environments, illuminating the potential of unifying evolutionary algorithms with reinforcement learning. This integration of discrete semantic search and continuous parameter updates provides a self-reinforcing framework that facilitates more effective LLM alignment.

Xinyu Lu, Kaiqi Zhang, Jinglin Yang +6

Chinese Information Processing Laboratory, Institute of Software, Chinese Academy of Sciences · University of Chinese Academy of Sciences · Institute of Information Engineering, Chinese Academy of Sciences +2

RL for Language Model ReasoningReinforcement Learning with Verifiable RewardsPrompt OptimizationSparse-Reward RL
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Mar 22, 2026

Prompt replay: speeding up grpo with on-policy reuse of high-signal prompts

Reinforcement learning with verifiable rewards (RLVR) plays a crucial role in expanding the capacities of LLM reasoning, but GRPO-style training is dominated by expensive rollouts and wastes compute on unusable prompts. We propose Prompt Replay, an overhead-free online data selection method for GRPO that reuses prompts only (not trajectories), to preserve on-policy optimization. After each step, we insert prompts with medium difficulty into a buffer, and prioritize prompts closer to a pass rate of 0.5 (half answers correct, half wrong) to maximize the advantage, thus learning signal. Training batches are formed by mixing reused prompts with fresh samples, with cooldown steps and max reuse times controlling aggressiveness vs risk of overfitting. Across multiple model families (Llama-3.2- 3B, Qwen3-8B) and training datasets (Dolci, Polaris), evaluated using average accuracy on six standard math benchmarks, Prompt Replay reduces zero-variance prompts, increases mean absolute advantage and shows faster initial accuracy gains. Yet, it plateaus and converges with the baseline, as too aggressive configuration was used. The method is most efficient when the rollouts are the primary bottleneck and the dataset is difficult for the model. We additionally observe that Qwen2.5-Math can exhibit spurious-reward effects that invalidates ablations, raising a warning signal for using it as a sole testbed for GRPO method research.

Andrei Baroian, Rutger Berger

Leiden Institute of Advanced Computer Science Leiden University

Prompt Selection for RLRL Post-TrainingGroup Relative Policy OptimizationReinforcement Learning with Verifiable Rewards
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Mar 22, 2026

WIST: Web-Grounded Iterative Self-Play Tree for Domain-Targeted Reasoning Improvement

Recent progress in reinforcement learning with verifiable rewards (RLVR) offers a practical path to self-improvement of language models, but existing methods face a key trade-off: endogenous self-play can drift over iterations, while corpus-grounded approaches rely on curated data environments. We present WIST, a Web-grounded Iterative Self-play Tree framework for domain-targeted reasoning improvement that learns directly from the open web without requiring any pre-arranged domain corpus. WIST incrementally expands a domain tree for exploration, and retrieves and cleans path-consistent web corpus to construct a controllable training environment. It then performs Challenger--Solver self-play with verifiable rewards, and feeds learnability signals back to update node posteriors and guide subsequent exploration through an adaptive curriculum. Across four backbones, WIST consistently improves over the base models and typically outperforms both purely endogenous self-evolution and corpus-grounded self-play baselines, with the Overall gains reaching +9.8 (Qwen3-4B-Base) and +9.7 (OctoThinker-8B). WIST is also domain-steerable, improving Qwen3-8B-Base by +14.79 in medicine and Qwen3-4B-Base by +5.28 on PhyBench. Ablations further confirm the importance of WIST's key components for stable open-web learning. Our Code is available at https://github.com/lfy-123/WIST.

Fangyuan Li, Pengfei Li, Shijie Wang +4

Harbin Institute of Technology · Shanghai Innovation Institute · Shanghai Artificial Intelligence Laboratory

Language Model Self-ImprovementRL for Language Model ReasoningSelf-Play RLReinforcement Learning with Verifiable RewardsCurriculum RL
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Mar 21, 2026

RLVR Training of LLMs Does Not Improve Thinking Ability for General QA: Evaluation Method and a Simple Solution

Reinforcement learning from verifiable rewards (RLVR) stimulates the thinking processes of large language models (LLMs), substantially enhancing their reasoning abilities on verifiable tasks. It is often assumed that similar gains should transfer to general question answering (GQA), but this assumption has not been thoroughly validated. To assess whether RLVR automatically improves LLM performance on GQA, we propose a Cross-Generation evaluation framework that measures the quality of intermediate reasoning by feeding the generated thinking context into LLMs of varying capabilities. Our evaluation leads to a discouraging finding: the efficacy of the thinking process on GQA tasks is markedly lower than on verifiable tasks, suggesting that explicit training on GQA remains necessary in addition to training on verifiable tasks. We further observe that direct RL training on GQA is less effective than RLVR. Our hypothesis is that, whereas verifiable tasks demand robust logical chains to obtain high rewards, GQA tasks often admit shortcuts to high rewards without cultivating high-quality thinking. To avoid possible shortcuts, we introduce a simple method, Separated Thinking And Response Training (START), which first trains only the thinking process, using rewards defined on the final answer. We show that START improves both the quality of thinking and the final answer across several GQA benchmarks and RL algorithms.

Kaiyuan Li, Jing-Cheng Pang, Yang Yu

National Key Laboratory for Novel Software Technology & School of Artificial Intelligence, Nanjing University, China · Polixir.ai, China · Huawei Technologies Co., Ltd., China

Language Model Reasoning EvaluationRL for Language Model ReasoningReinforcement Learning with Verifiable RewardsQuestion AnsweringLLM Evaluation
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Mar 20, 2026

Human-Level Text-to-SQL via Reinforcement Learning on Verified Data, Without Pipeline Engineering

Translating natural language questions to SQL queries (Text-to-SQL) is a long-standing problem in database research. Recent efforts have focused on improving accuracy by building increasingly complex multi-stage large LLM pipelines, layering task decomposition, schema linking, and model-based query selection on top of an LLM. Despite this growing complexity, a substantial gap (>10%) between such systems and human experts persists on benchmarks, suggesting that pipeline engineering alone has hit a ceiling. We show that human-level Text-to-SQL performance is achievable by fine-tuning an LLM using RLVR on clean data, without pipeline components. In this paper, we identified the dominant bottleneck for RLVR on Text-to-SQL: existing training data contains pervasive annotation errors that mislead optimization. To address this, we developed a multi-round, expert-driven verification pipeline and used it to curate BIRD-Platinum, a dataset of 2.5k verified instances sampled from BIRD Train, with errors corrected in 61% of instances. We show that fine-tuning Qwen3-235B on BIRD-Platinum yields consistent improvements (11-16%) over BIRD Train on Arcwise-Plat (an expert-verified version of BIRD) and Spider2, outperforming SOTA open-source systems by 0.6-16%. Furthermore, we diagnosed two failure modes of standard RLVR on Text-to-SQL. We find that (1) result-based rewards have non-trivial false positive rates, and (2) models systematically ignore the external knowledge in BIRD-style problems. To address them, we propose ReViSQL-BIRD, a specialized reward shaping method that combines result-based rewards with SQL equivalence verification and leverages process rewards for incentivizing external-knowledge use. We fine-tuned Kimi-K2.6 with ReViSQL-BIRD. On Arcwise-Plat, ReViSQL-BIRD-K2.6 is the first method to achieve human-level accuracy (92.96%), outperforming top five open-source systems by 10-22%.

Yuxuan Zhu, Tengjun Jin, Yoojin Choi +1

University of Illinois · Bridgewater AIA Labs

Text-to-SQLReinforcement Learning with Verifiable RewardsReward Shaping
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Mar 19, 2026

OS-Themis: A Scalable Critic Framework for Generalist GUI Rewards

Reinforcement Learning (RL) has the potential to improve the robustness of GUI agents in stochastic environments, yet training is highly sensitive to the quality of the reward function. Existing reward approaches struggle to achieve both scalability and performance. To address this, we propose OS-Themis, a scalable and accurate multi-agent critic framework. Unlike a single judge, OS-Themis decomposes trajectories into verifiable milestones to isolate critical evidence for decision making and employs a review mechanism to strictly audit the evidence chain before making the final verdict. To facilitate evaluation, we further introduce OmniGUIRewardBench (OGRBench), a holistic cross-platform benchmark for GUI outcome rewards, where all evaluated models achieve their best performance under OS-Themis. Extensive experiments on AndroidWorld show that OS-Themis yields a 10.3% improvement when used to support online RL training, and a 6.9% gain when used for trajectory validation and filtering in the self-training loop, highlighting its potential to drive agent evolution.

Zehao Li, Zhenyu Wu, Yibo Zhao +11

University of Science and Technology of China · Shanghai AI Laboratory · CUHK MMLab +2

Reward ModelingRL for GUI AgentsReinforcement Learning with Verifiable Rewards
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Mar 19, 2026

Context Bootstrapped Reinforcement Learning

Reinforcement Learning from Verifiable Rewards (RLVR) suffers from exploration inefficiency, where models struggle to generate successful rollouts, resulting in minimal learning signal. This challenge is particularly severe for tasks that require the acquisition of novel reasoning patterns or domain-specific knowledge. To address this, we propose Context Bootstrapped Reinforcement Learning (CBRL), which augments RLVR training by stochastically prepending few-shot demonstrations to training prompts. The injection probability follows a curriculum that starts high to bootstrap early exploration, then anneals to zero so the model must ultimately succeed without assistance. This forces the policy to internalize reasoning patterns from the demonstrations rather than relying on them at test time. We validate CBRL across two model families and five Reasoning Gym tasks. Our results demonstrate that CBRL consistently improves success rate, provides better exploration efficiency, and is algorithm-agnostic. We further demonstrate CBRL's practical applicability on Q, a domain-specific programming language that diverges significantly from mainstream language conventions.

Saaket Agashe, Jayanth Srinivasa, Gaowen Liu +2

University of California, Santa Barbara · Cisco Research

RL for Language Model ReasoningReinforcement Learning with Verifiable RewardsRL for Code GenerationCurriculum RL
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Mar 19, 2026

Discounted Beta-Bernoulli Reward Estimation for Sample-Efficient Reinforcement Learning with Verifiable Rewards

Reinforcement learning with verifiable rewards (RLVR) has emerged as an effective post-training paradigm for improving the reasoning capabilities of large language models. However, existing group-based RLVR methods often suffer from severe sample inefficiency. This inefficiency stems from reliance on point estimation of rewards from a small number of rollouts, leading to high estimation variance, variance collapse, and ineffective utilization of generated responses. In this work, we reformulate RLVR from a statistical estimation perspective by modeling rewards as samples drawn from a policy-induced distribution and casting advantage computation as the problem of estimating the reward distribution from finite data. Building on this view, we propose Discounted Beta-Bernoulli (DBB) reward estimation, which leverages historical reward statistics for the non-stationary distribution. Although biased, the resulting estimator exhibits reduced and stable variance, theoretically avoids estimated variance collapse, and achieves lower mean squared error than standard point estimation. Extensive experiments across six in-distribution and three out-of-distribution reasoning benchmarks demonstrate that GRPO with DBB consistently outperforms naive GRPO, achieving average Acc@8 improvements of 3.22/2.42 points in-distribution and 12.49/6.92 points out-of-distribution on the 1.7B and 8B models, respectively, without additional computational cost or memory usage.

Haechan Kim, Soohyun Ryu, Gyouk Chu +2

Kim Jaechul Graduate School of AI, KAIST, Daejeon, South Korea · KRAFTON, Seoul, South Korea · AITRICS, Seoul, South Korea

Reinforcement LearningRL for Language Model ReasoningReinforcement Learning with Verifiable RewardsSample-Efficient RL
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Mar 18, 2026

RAWR: Reward Assignment Without Rollouts in Verifiable Domains

Understanding and evaluating multi-step reasoning in LLMs at the level of individual steps remains a key challenge. Process reward models (PRMs) provide a solution by scoring each step, enabling fine-grained supervision and improved reliability. However, training them requires costly human annotation or computationally intensive rollout-based labeling. To solve this, we introduce MCNIG, a scalable method for automatically labeling the quality of individual reasoning steps in any verifiable domain. Its step score, net information gain (NetIG), improves upon single-reference information gain (IG) by comparing the most-supported correct answer against the most-supported incorrect one, yielding a robust signal even for long and structured outputs like code and SQL, where IG fails. We show that the signal produced by MCNIG correlates with human judgments of step quality, and we apply MCNIG labels to train PRMs that achieve the best average best-of-K accuracy across eight benchmarks spanning mathematics, code generation, text-to-SQL, and scientific QA. Crucially, MCNIG generates no rollouts, cutting labeling complexity to O(N) and making it up to X times cheaper than rollout-based methods at comparable label quality, which makes large-scale process supervision practical.

Corentin Royer, Anna Hedström, Debarun Bhattacharjya +3

International Business Machines · ETH AI Center · Lirio +1

Process Reward ModelsReinforcement Learning with Verifiable RewardsProcess SupervisionStep-Level Credit AssignmentLLM Reasoning
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Mar 17, 2026

Dual Consensus: Escaping from Spurious Majority in Unsupervised RLVR via Two-Stage Vote Mechanism

Current label-free RLVR approaches for large language models (LLMs), such as TTRL and Self-reward, have demonstrated effectiveness in improving the performance of LLMs on complex reasoning tasks. However, these methods rely heavily on accurate pseudo-label estimation and converge on spurious yet popular answers, thereby trapping in a dominant mode and limiting further improvements. Building on this, we propose Dual Consensus Reinforcement Learning (DCRL), a novel self-supervised training method which is capable of generating more reliable learning signals through a two-stage consensus mechanism. The model initially acts as an anchor, producing dominant responses; then it serves as an explorer, generating diverse auxiliary signals via a temporary unlearning process. The final training target is derived from the harmonic mean of these two signal sets. Notably, the process operates entirely without external models or supervision. Across eight benchmarks and diverse domains, DCRL consistently improves Pass@1 over majority vote while yielding more stable training dynamics. These results demonstrate that DCRL establishes a scalable path toward stronger reasoning without labels.

Kaixuan Du, Meng Cao, Hang Zhang +3

School of Automation Science and Electrical Engineering, Beihang University

RL for Language Model ReasoningSelf-Training for Language ModelsReinforcement Learning with Verifiable RewardsSelf-Consistency in Language Models
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Mar 17, 2026

Execution-Grounded Credit Assignment for GRPO in Code Generation

Critic-free reinforcement learning with verifiable rewards (RLVR) improves code generation by optimizing unit-test pass rates, but GRPO-style updates suffer from coarse credit assignment: a single outcome signal is spread uniformly across long programs even when failure stems from a localized semantic error. We propose Execution-Grounded Credit Assignment (EGCA), which localizes GRPO updates using execution traces. For programs that satisfy algorithmic constraints but fail tests, EGCA executes the candidate and a canonical reference solution (curated once offline; used for analysis, not supervision) under identical instrumentation, identifies the earliest semantic divergence, and assigns advantage only to the corresponding token span while masking downstream tokens. EGCA is a drop-in modification requiring no critic, auxiliary loss, or learned verifier, yielding 82.1% pass@1 on HumanEval (+3.1 over GRPO) and 68.9% on MBPP (+1.5) with 18% wall-clock overhead.

Abhijit Kumar, Natalya Kumar, Shikhar Gupta

RL for Code GenerationCredit AssignmentToken-Level Credit AssignmentReinforcement Learning with Verifiable RewardsExecution-Guided Code Generation
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