ICML 2026 论文列表

International Conference on Machine Learning

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6,341篇论文

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Estimation of Treatment Effects Under Nonstationarity via the Truncated Policy Gradient Estimator

Ramesh Johari, Tianyi Peng, Wenqian Xing

展开摘要

Randomized experiments (or A/B tests) are widely used to evaluate interventions in dynamic systems such as recommendation platforms, marketplaces, and digital health. In these settings, interventions affect both current and future system states, so estimating the global average treatment effect (GATE) requires accounting for temporal dynamics, which is especially challenging in the presence of nonstationarity; existing approaches suffer from high bias, high variance, or both. In this paper, we address this challenge via the novel Truncated Policy Gradient (TPG) estimator, which replaces instantaneous outcomes with short-horizon outcome trajectories. The estimator admits a policy gradient interpretation: it is a truncation of the first-order approximation to the GATE, yielding provable reductions in bias and variance in nonstationary Markovian settings. We further establish a central limit theorem for the TPG estimator and develop a consistent variance estimator that remains valid under nonstationarity with single-trajectory data. We validate our theory with two real-world case studies. The results show that relative to existing approaches, a well-calibrated TPG estimator can achieve a favorable balance between bias and variance in nonstationary settings, highlighting the value of the policy-gradient perspective for designing effective estimators under complex dynamics.

Poster
CoCoEdit: Content-Consistent Image Editing via Region Regularized Reinforcement Learning

Yuhui Wu, Chenxi Xie, Ruibin Li, Liyi Chen, Qiaosi Yi, Lei Zhang

展开摘要

Image editing has achieved impressive results with the development of large-scale generative models. However, existing models mainly focus on the editing effects of intended objects and regions, often leading to unwanted changes in unintended regions. We present a post-training framework for $\textbf{Co}$ntent-$\textbf{Co}$nsistent $\textbf{Edit}$ing ($\textbf{CoCoEdit}$) by using region regularized reinforcement learning. We first augment existing editing datasets with refined instructions and masks, from which 40K diverse and high quality samples are curated as training set. We introduce a pixel-level similarity reward that complements MLLM-based rewards, enabling models to ensure both editing quality and content consistency during the editing process. To overcome the spatial-agnostic nature of the rewards, we propose a region-based regularizer, aiming to preserve non-edited regions for high-reward samples while encouraging editing effects for low-reward samples. For evaluation, we annotate editing masks for GEdit-Bench and ImgEdit-Bench, introducing pixel-level similarity metrics to measure content consistency and editing quality. Applying CoCoEdit to Qwen-Image-Edit and FLUX-Kontext, we achieve not only superior editing scores to state-of-the-art models, but also significantly better content consistency, measured by PSNR/SSIM metrics and human subjective ratings. Codes, data and models of CoCoEdit can be found at https://github.com/langmanbusi/CoCoEdit.

Poster
VIPO: Value Function Inconsistency Penalized Offline Reinforcement Learning

Xuyang Chen, Keyu Yan, Guojian Wang, Lin Zhao

展开摘要

Offline reinforcement learning (RL) learns effective policies from pre-collected datasets, offering a practical solution for applications where online interactions are risky or costly. Model-based approaches are particularly advantageous for offline RL, owing to their data efficiency and generalizability. However, due to inherent model errors, model-based methods often artificially introduce conservatism guided by heuristic uncertainty estimation, which can be unreliable. In this paper, we introduce VIPO, a novel model-based offline RL algorithm that incorporates self-supervised feedback from value estimation to enhance model training. Specifically, the model is learned by additionally minimizing the inconsistency between the value learned directly from the offline data and the value estimated from the model. We perform comprehensive evaluations from multiple perspectives to show that VIPO can learn a highly accurate model efficiently and consistently outperform existing methods. In particular, it achieves state-of-the-art performance on almost all tasks in both D4RL and NeoRL benchmarks. Overall, VIPO offers a \textit{general framework} that can be readily integrated into existing model-based offline RL algorithms to systematically enhance model accuracy. Our code is available at~\url{https://anonymous.4open.science/r/vipo2025-8FD4}.

Poster
The Role of Target Update Frequencies in Q-Learning

Simon Weissmann, Tilman Aach, Benedikt Wille, Sebastian Kassing, Leif Döring

展开摘要

The target network update frequency (TUF) is a central stabilization mechanism in (deep) Q-learning. However, its selection remains poorly understood and is often treated merely as another tunable hyperparameter rather than as a principled design decision. This work provides a theoretical analysis of target fixing in tabular Q-learning through the lens of approximate dynamic programming. We view periodic Q-learning as a nested optimization scheme in which each outer iteration applies an inexact Bellman optimality operator, approximated by a generic inner loop optimizer. Rigorous theory yields a finite-time convergence analysis for the asynchronous sampling setting, specializing to stochastic gradient descent in the inner loop. Our results deliver an explicit characterization of the bias–variance trade-off induced by the target update period, showing how to optimally set this critical hyperparameter. We prove that constant target update schedules are suboptimal, incurring a logarithmic overhead in sample complexity that is entirely avoidable with adaptive schedules. Our analysis shows that the optimal target update frequency decreases geometrically over the course of the learning process.

Poster
Test-Time Reinforcement Learning for Flow Matching

Jili Chen, Changqin Huang, Qionghao Huang, Yaxin Tu, Zhonglong Zheng, Xiaodi Huang

展开摘要

Flow-matching has emerged as a leading framework for high-fidelity text-to-image generation. However, its alignment with human preferences through RL is often hindered by substantial computational overhead. In this paper, we introduce Flow-TTRL, the first test-time reinforcement learning framework that achieves alignment on the fly. Our approach reinterprets intermediate latent representations as an implicit policy and utilizes SDE-based rollouts to explore high-reward trajectories within the learned vector field. Specifically, we propose a two-stage optimization strategy: Proximal Reward Difference Prediction (PRDP) ensures structural stability in high-noise regimes through pairwise reward regression, while Group Relative Policy Optimization (GRPO) refines fine-grained aesthetic details by maximizing relative advantages within sampled candidate groups. Experimental results show that Flow-TTRL significantly boosts aesthetic quality, text-image alignment, and human preference across diverse backbones. On the GenEval benchmark, Flow-TTRL elevates the accuracy of SD 3.5-Medium from 63\% to 87\% and Flux.1 Dev from 66\% to 83\%. Furthermore, our framework achieves an average gain of 15\% to 20\% across T2I-CompBench metrics, delivering performance comparable to state-of-the-art RL-based fine-tuning methods without the need for additional fine-tuning. Our code is available at ~\url{https://github.com/TheShy-Dream/Flow-TTRL}.

Poster
Positive–Unlabeled Reinforcement Learning Distillation for On-Premise Small Models

Zhiqiang Kou, Junyang Chen, Xin-Qiang Cai, Xiaobo Xia, Ming-Kun Xie, Dong-Dong Wu, Biao Liu, Yuheng Jia, Xin Geng, Masashi Sugiyama, Tat-Seng Chua

展开摘要

Due to constraints on privacy, cost, and latency, on-premise deployment of small models is increasingly common. However, most practical pipelines stop at supervised fine-tuning (SFT) and fail to reach the reinforcement learning (RL) alignment stage. The main reason is that RL alignment typically requires either expensive human preference annotation or heavy reliance on high-quality reward models with large-scale API usage and ongoing engineering maintenance, both of which are ill-suited to on-premise settings. To bridge this gap, in this paper, we propose a positive-unlabeled (PU) RL distillation method for on-premise small-model deployment. Without human-labeled preferences or a reward model, our method distills the teacher’s preference-optimization capability from black box generations into a locally trainable student. For each prompt, we query the teacher once to obtain an anchor response, locally sample multiple student candidates, and perform anchor-conditioned self-ranking to induce pairwise or listwise preferences, enabling a fully local training loop via direct preference optimization or group relative policy optimization. Theoretical analysis justifies that the induced preference signal by our method is order-consistent and concentrates on near-optimal candidates, supporting its stability for preference optimization. Experiments demonstrate that our method achieves consistently strong performance under a low-cost setting.

Poster
Reparameterization Flow Policy Optimization

Hai Zhong, Zhuoran Li, Xun Wang, Longbo Huang

展开摘要

Reparameterization Policy Gradient (RPG) has emerged as a powerful paradigm for model-based reinforcement learning, enabling high sample efficiency by backpropagating gradients through differentiable dynamics. However, prior RPG approaches have been predominantly restricted to Gaussian policies, limiting their performance and failing to leverage recent advances in generative models. In this work, we identify that flow policies, which generate actions via differentiable ODE integration, naturally align with the RPG framework, a connection not established in prior work. Yet, naively realizing this synergy is non-trivial: it often suffers from training instability and a lack of exploration. We propose Reparameterization Flow Policy Optimization (RFO). RFO computes policy gradients by backpropagating jointly through the flow generation process and system dynamics, unlocking high sample efficiency without requiring intractable log-likelihood calculations. RFO includes two tailored regularization terms for stability and exploration. We also propose a variant of RFO with action chunking. Extensive experiments on diverse locomotion and manipulation tasks—involving both rigid and soft bodies with state or visual inputs—demonstrate the effectiveness of RFO. Notably, on a challenging locomotion task controlling a soft-body quadruped, RFO achieves almost $2\times$ the reward of the state-of-the-art baseline.

Poster
Unsupervised Hierarchical Skill Discovery

Damion Harvey, Geraud Nangue Tasse, Benjamin Rosman, Branden Ingram, Steven James

展开摘要

We consider the problem of unsupervised skill segmentation and hierarchical structure discovery in reinforcement learning. While recent approaches have sought to segment trajectories into reusable skills or options, most rely on action labels, rewards, or handcrafted annotations, limiting their applicability. We propose a method that segments unlabelled trajectories into skills and induces a hierarchical structure over them using a grammar-based approach. The resulting hierarchy captures both low-level behaviours and their composition into higher-level skills. We evaluate our approach in high-dimensional, pixel-based environments, including Craftax and the full, unmodified version of Minecraft. Using metrics for skill segmentation, reuse, and hierarchy quality, we find that our method consistently produces more structured and semantically meaningful hierarchies than existing baselines. Furthermore, as a proof of concept, we demonstrate that these discovered hierarchies accelerate and stabilise learning on downstream reinforcement learning tasks.

Poster
Addressing Semantic Blind Spots in Text-to-SQL via Component Pre-generation and AST Matching Rewards

Xingyu Ma, Xin Tian, Lingxiang Wu, Xuepeng Wang, Zhilin Zhang, Xueming Tang, Jinqiao Wang

展开摘要

In recent years, significant advancements in large language models have greatly propelled the development of Text-to-SQL tasks. However, due to the token-by-token sequential generation mechanism employed by these models, they encounter a semantic blind spot problem with respect to pending SQL components—the parts of the SQL query yet to be generated. Specifically, language models are unable to effectively utilize the semantic information of these pending SQL components during the generation of the final SQL query, which poses considerable challenges for generating complex SQL statements. To address this issue, we propose a novel thought process based on SQL components pre-generation and design a maximum connected subtree matching reward mechanism leveraging the SQL abstract syntax tree to improve the accuracy of local component generation. Extensive experiments demonstrate that, under comparable model parameter scales, our training approach achieves significant advantages, effectively enhancing the generation of complex SQL queries. Our method attains an execution accuracy EX of 65.78% on the BIRD-dev dataset and achieves state-of-the-art performance on the Spider-syn datasets.

Poster
From Static Constraints to Dynamic Adaptation: Sample-Level Constraint Relaxation for Offline-to-Online Reinforcement Learning

Lipeng Zu, YU QIAN, Shayok Chakraborty, Xiaonan Zhang

展开摘要

Offline-to-online reinforcement learning (O2O RL) faces a central challenge between retaining offline conservatism and adapting to online feedback under distribution shift. This challenge arises because data behavior evolves during fine-tuning, rendering data origin a misleading basis for constraint handling and thereby leading to objective–data mismatch. We therefore propose Dynamic Alignment for RElaxation (DARE), a distribution-aware framework for sample-level constraint relaxation based on the behavioral consistency with a behavior model. To our knowledge, DARE is the first to condition constraint relaxation on behavioral consistency via a posterior-induced exchange mechanism, moving beyond a binary offline/online data distinction. Importantly, DARE requires only per-sample behavioral alignment, enabling instantiation on top of many offline algorithms with flexible choices of behavior models and fine-tuning objectives. We provide a theoretical analysis showing that behavior-based sample exchange consistently improves the distinction between offline-like and online-like subsets. Experiments on D4RL demonstrate that DARE consistently improves fine-tuning stability and achieves superior final performance over strong offline-to-online baselines. (The code is publicly available at \url{https://github.com/lpzu/DARE}.)

Poster
BiTrajDiff: Bidirectional Trajectory Generation with Diffusion Models for Offline Reinforcement Learning

Yunpeng Qing, Yixiao Chi, Shuo Chen, Shunyu Liu, Kexuan Zhou, Sixu Lin, Litao Liu, Changqing Zou

展开摘要

Offline Reinforcement Learning (RL) relies on static datasets and often enforces conservative constraints to mitigate out-of-distribution errors, but this inevitably gives rise to learning dataset biases and limited behavioral generalization. Recent Data Augmentation (DA) methods leverage generative models to enrich offline data, yet they mainly operate within a single rollout paradigm and tend to preserve the original trajectory-level connectivity of the dataset. As a result, such methods often introduce local variations and fail to recover connections between distinct behavior patterns. In this paper, we propose Bidirectional Trajectory Diffusion (BiTrajDiff), a novel DA framework that explicitly addresses this limitation. BiTrajDiff decomposes trajectory synthesis into two independent diffusion processes that generate forward-future and backward-history segments conditioned on shared intermediate anchor states. By stitching the generated segments at these anchors, BiTrajDiff can synthesize trajectories that bridge disconnected behavior patterns and recover global trajectory-level connectivity absent from the original data. Extensive experiments demonstrate that BiTrajDiff consistently outperforms advanced DA methods across a range of offline RL backbones. Our code is available at [https://github.com/Plankson/BiTrajDiff](https://github.com/Plankson/BiTrajDiff).

Poster
Conversation for Non-verifiable Learning: Self-Evolving Large Language Models through Meta-Evaluation

Yuan Sui, Bryan Hooi

展开摘要

Training large language models (LLMs) for non-verifiable tasks—such as creative writing, dialogue, and ethical reasoning—remains challenging due to the absence of ground-truth labels. While LLM-as-Judge approaches offer a scalable alternative to human feedback, they face a fundamental limitation: performance is constrained by the evaluator's own quality. If the judge cannot recognize good solutions, it cannot provide useful training signals, and evaluation biases (e.g., favoring verbosity over quality) remain unaddressed. This motivates meta-evaluation—the ability to evaluate and improve the evaluator itself. We introduce CoNL, a framework that unifies generation, evaluation, and meta-evaluation through multi-agent self-play. Our key insight: critique quality can be measured by whether it helps others improve their solutions. In CoNL, multiple agents sharing the same policy engage in structured conversations to propose, critique, and revise solutions. Critiques that enable other agents' solution improvements earn a diagnostic reward, creating explicit supervision for meta-evaluation and enabling joint optimization of generation and judging capabilities through self-play, without external judges or ground truth. Experiments on various benchmarks show that CoNL achieves consistent improvements over self-rewarding baselines while maintaining stable training.

Poster
MMKU-Bench: A Multimodal Update Benchmark for Diverse Visual Knowledge

Baochen Fu, Yuntao Du, Cheng Chang, Baihao Jin, Wenzhi Deng, Muhao Xu, Hongmei Yan, Weiye Song, Yi Wan

展开摘要

As real-world knowledge continues to evolve, the parametric knowledge acquired by multimodal models during pretraining becomes increasingly difficult to remain consistent with real-world knowledge. Existing research on multimodal knowledge updating focuses only on learning previously unknown knowledge, while overlooking the need to update knowledge that the model has already mastered but that later changes; moreover, evaluation is limited to the same modality, lacking a systematic analysis of cross-modal consistency. To address these issues, this paper proposes MMKU-Bench, a comprehensive evaluation benchmark for multimodal knowledge updating, which contains over 25k knowledge instances and more than 49k images, covering two scenarios, updated knowledge and unknown knowledge, thereby enabling comparative analysis of learning across different knowledge types. On this benchmark, we evaluate a variety of representative approaches, including supervised fine-tuning (SFT), reinforcement learning from human feedback (RLHF), and knowledge editing (KE). Experimental results show that SFT and RLHF are prone to catastrophic forgetting, while KE better preserve general capabilities but exhibit clear limitations in continual updating. Overall, MMKU-Bench provides a reliable and comprehensive evaluation benchmark for multimodal knowledge updating, advancing progress in this field. The code and dataset are available at https://github.com/baochenfu/MMKU-Bench.

Poster
One Tool Is Enough: Reinforcement Learning of LLM Agents for Repository-Level Code Navigation

Zhaoxi Zhang, Yitong Duan, Yanzhi Zhang, Yiming Xu, Zhixiang Wang, Kun Liang, Weikang Li, Jiahui Liang, Deguo Xia, Jizhou Huang, Jiyan He, Shuxin Zheng, Yunfang Wu

展开摘要

Locating files and functions requiring modification in large software repositories is challenging due to their scale and structural complexity. Existing LLM-based methods typically treat this as a repository-level retrieval task and rely on multiple auxiliary tools, which often overlook code execution logic and complicate model control. We propose RepoNavigator, an LLM agent equipped with a single execution-aware tool: jumping to the definition of an invoked symbol. This unified design reflects the actual flow of code execution while simplifying tool manipulation. RepoNavigator is trained end-to-end via Reinforcement Learning (RL) directly from a base pretrained model, without relying on closed-source distillation. Experiments demonstrate that RL-trained RepoNavigator achieves state-of-the-art performance, with the 7B model outperforming 14B baselines, the 14B model surpassing 32B competitors, and the 32B model exceeding closed-source models such as GPT-5 on most metrics. These results confirm that integrating a single, structurally grounded tool with RL training provides an efficient and scalable solution for repository-level issue localization.

Poster
Approximation of Log-Partition Function in Policy Mirror Descent Induces Implicit Regularization for LLM Post-Training

Zhenghao Xu, Qin Lu, Changlong Yu, Tuo Zhao

展开摘要

Policy mirror descent (PMD) provides a principled framework for reinforcement learning (RL) by iteratively solving KL-regularized policy improvement subproblems. While this approach has been adopted in training advanced LLMs such as Kimi K1.5/K2, the ideal closed-form PMD updates require reliable partition function estimation, a significant challenge when working with limited rollouts in the vast action spaces of LLMs. We investigate a practical algorithm, termed PMD-mean, that approximates the log-partition term with the mean reward under the sampling policy and performs regression in log-policy space. Specifically, we characterize the population solution of PMD-mean and demonstrate that it implicitly optimizes mirror descent subproblems with an adaptive mixed KL--$\chi^2$ regularizer. This additional $\chi^2$ regularization constrains large probability changes, producing more conservative updates when expected rewards are low and enhancing robustness against finite-sample estimation errors. Experiments on math reasoning tasks show that PMD-mean improves stability and remains competitive in the stale-rollout settings while enabling higher throughput through larger rollout batches. These findings deepen our understanding of PMD-mean and illuminate pathways toward principled improvements in RL algorithms for LLMs. Code is available at https://github.com/horizon-llm/OpenKimi.

Poster
UDM-GRPO: Stable and Efficient Group Relative Policy Optimization for Uniform Discrete Diffusion Models

Jiaqi Wang, Haoge Deng, Ting Pan, Yang Liu, Chengyuan Wang, Fan Zhang, Yonggang Qi, Xinlong Wang

展开摘要

Uniform Discrete Diffusion Model (UDM) has recently emerged as a promising paradigm for discrete generative modeling; however, its integration with reinforcement learning remains largely unexplored. We observe that naively applying GRPO to UDM leads to training instability and marginal performance gains. To address this, we propose **UDM-GRPO**, the first framework to integrate UDM with RL. Our method is guided by two key insights: (i) treating the final clean sample as the action provides more accurate and stable optimization signals; and (ii) reconstructing trajectories via the diffusion forward process better aligns probability paths with the pretraining distribution. Additionally, we introduce two strategies, Reduced-Step and CFG-Free, to further improve training efficiency. **UDM-GRPO** significantly improves base model performance across multiple T2I tasks. Notably, GenEval accuracy improves from $69\\%$ to $96\\%$ and PickScore increases from $20.46$ to $23.81$, achieving state-of-the-art performance in both continuous and discrete settings. On the OCR benchmark, accuracy rises from $8\\%$ to $57\\%$, further validating the generalization ability of our method. Code is available at https://github.com/Yovecent/UDM-GRPO.

Spotlight
MVR-cache: Optimizing Semantic Caching via Multi-Vector Retrieval and Learned Prompt Segmentation

Ali Noshad, Zishan Zheng, Yinjun Wu

展开摘要

To reduce LLM costs and latency, semantic caching systems must accurately identify when a new prompt matches a cached one. Current methods often rely on simplistic similarity measures, which limit their effectiveness. We introduce MVR-cache, a novel semantic caching approach that significantly improves retrieval accuracy by integrating Multi-Vector Retrieval (MVR). MVR-cache is built upon a learnable segmentation model that intelligently splits prompts, enabling fine-grained similarity comparisons via MaxSim. We derive the model's training objective from a rigorous theoretical analysis. This can ensure that optimizing this objective directly maximizes cache hits under strict correctness constraints. To solve the resulting non-differentiable combinatorial optimization problem, we leverage a reinforcement learning-based training strategy with the theoretically grounded objectives as the reward. Experimental results on established benchmarks across diverse tasks confirm that in comparison to the state-of-the-art, MVR-cache consistently increases the cache hit rates by up to 37\% while maintaining the same correctness guarantees. MVR-cache is available at https://github.com/PKU-SDS-lab/MVR-Cache

Poster
SpikeVLA: Vision-Language-Action Models with Spiking Neural Networks

Ruiqi Song, Dujun Nie, Siyu Teng, Baiyong Ding, Xiaotong Zhang, Dong Li, Chenming Zhang, Yuchen Li, Hangbin Wu, Long Chen

展开摘要

Vision-Language-Action (VLA) models have become a central paradigm for embodied intelligence. However, most existing approaches are built on large-scale Transformers, resulting in substantial inference latency and energy consumption that limit their practical deployment in low-power, real-time scenarios. We propose SpikeVLA, an end-to-end spiking VLA framework for embodied navigation with energy-efficient inference, consisting of three key components. (i) a spiking vision encoder, Spike-V, that replaces dense continuous computation with event-driven spiking representations to reduce the energy cost of visual representation learning, (ii) a multimodal spiking large language model, Spike-L, that reformulates cross-modal reasoning with spiking dynamics and token-level event-driven sparsity to further lower inference overhead, and (iii) a spiking action policy network, Spike-A, that uses Laplacian-kernel population coding and end-to-end reinforcement learning to produce stable, robust continuous control under low-energy constraints. Experiments on multimodal interaction and robotic control tasks show that SpikeVLA significantly reduces energy consumption and computational overhead while maintaining competitive performance, highlighting its potential for low-power, real-time embodied intelligence.

Poster
Plan in Sandbox, Navigate in Open Worlds: Learning Physics-Grounded Abstracted Experience for Embodied Navigation

Zhixuan Shen, Jiawei DU, Ziyu Guo, Han Luo, Lilan Peng, Joey Tianyi Zhou, Haonan Luo, Tianrui Li

展开摘要

Vision-Language Models (VLMs) have demonstrated exceptional general reasoning capabilities. However, their performance in embodied navigation remains hindered by a scarcity of aligned open-world vision and robot control data. Despite simulators providing a cost-effective alternative for data collection, the inherent reliance on photorealistic simulations often limits the transferability of learned policies. To this end, we propose ***S**andbox-**A**bstracted **G**rounded **E**xperience* (***SAGE***), a framework that enables agents to learn within a physics-grounded semantic abstraction rather than a photorealistic simulation, mimicking the human capacity for mental simulation where plans are rehearsed in simplified physics abstractions before execution. *SAGE* operates via three synergistic phases: (1) *Genesis*: constructing diverse, physics-constrained semantic environments to bootstrap experience; (2) *Evolution*: distilling experiences through Reinforcement Learning (RL), utilizing a novel asymmetric adaptive clipping mechanism to stabilize updates; (3) *Navigation*: bridging the abstract policy to open-world control. We demonstrate that *SAGE* significantly improves planner-assisted embodied navigation, achieving a 53.21% LLM-Match Success Rate on A-EQA (+9.7% over baseline), while showing encouraging transfer to physical indoor robot deployment. Project page is available at: <https://frankzxshen.github.io/SAGE>.

Poster
SAGE: Shaping Anchors for Guided Exploration in RLVR of LLMs

Chanuk Lee, Minki Kang, Sung Ju Hwang

展开摘要

Recent studies observe that reinforcement learning with verifiable rewards (RLVR) reliably improves pass@1 on reasoning tasks, yet often fails to yield comparable gains in pass@k, raising the question of whether RLVR genuinely enables large language models to acquire novel reasoning abilities or merely enhances the efficiency of sampling reasoning modes already present in the base model. Prior analyses largely support the latter view, attributing this limitation to structural properties of standard RLVR objectives that result in insufficient exploration pressure. In this work, we argue that a central structural constraint arises from reverse-KL regularization, which stabilizes training but inherently anchors the policy to the reference distribution, thereby suppressing the emergence of alternative reasoning modes. However, we show that neither removing the KL term nor replacing it with forward-KL provides a satisfactory solution, as both disrupt the efficiency–coverage trade-off by either inducing reward hacking or allocating probability mass to off-target regions. To resolve this tension, we propose SAGE, a principled framework that enables controllable empirical support expansion by reshaping the reverse-KL anchor distribution itself through a guide function $q(x,y)$, achieving consistent improvements in both pass@1 and pass@k across challenging mathematical reasoning benchmarks.

Poster