ICML 2026 Papers

We introduce Reinforcement Learning (RL) with Adaptive Verifiable Environments (RLVE), an approach using verifiable environments that procedurally generate problems and provide algorithmically verifiable rewards, to scale up RL for language models (LMs). RLVE enables each verifiable environment to dynamically adapt its problem difficulty distribution to the policy model's capabilities as training progresses. In contrast, static data distributions often lead to vanishing learning signals when problems are either too easy or too hard for the policy. To implement RLVE, we create RLVE-Gym, a large-scale suite of 400 verifiable environments carefully developed through manual environment engineering. Using RLVE-Gym, we show that environment scaling, i.e., expanding the collection of training environments, consistently improves generalizable reasoning capabilities. RLVE with joint training across all 400 environments in RLVE-Gym yields a 3.37% absolute average improvement across six reasoning benchmarks, starting from one of the strongest 1.5B reasoning LMs. By comparison, continuing this LM's original RL training yields only a 0.49% average absolute gain despite using over 3x more compute. We release our code publicly.

Post-training of flow matching models—aligning the output distribution with a high-quality target—is mathematically equivalent to imitation learning. While Supervised Fine-Tuning mimics expert demonstrations effectively, it cannot correct policy drift in unseen states. Preference optimization methods address this but require costly preference pairs or reward modeling. We propose Flow Matching Adversarial Imitation Learning (FAIL), which minimizes policy-expert divergence through adversarial training without explicit rewards or pairwise comparisons. We derive two algorithms: FAIL-PD exploits differentiable ODE solvers for low-variance pathwise gradients, while FAIL-PG provides a black-box alternative for discrete or computationally constrained settings. Fine-tuning FLUX with only 13,000 demonstrations from Nano Banana pro, FAIL achieves competitive performance on prompt following and aesthetic benchmarks. Furthermore, the framework generalizes effectively to discrete image and video generation, and functions as a robust regularizer to mitigate reward hacking in reward-based optimization.

The Policy-Space Response Oracles (PSRO) framework scales equilibrium computation to large zero-sum games by iteratively expanding a restricted strategy set using deep reinforcement learning (DRL). A central challenge is to construct, under limited computational budgets, a small strategy population whose induced game well approximates the full game. Existing PSRO variants typically expand the population using best responses to meta-strategies computed from restricted-game payoffs, which can lead to inefficient expansions that provide limited global improvement. We propose to guide population expansion by directly evaluating the post-expansion population quality. Specifically, we adopt Population Exploitability (PE) to measure how well a restricted strategy set represents the full game, and introduce a two-phase exploration--selection framework that explicitly minimizes PE during expansion. We instantiate this framework as Global PSRO, a practical DRL-based algorithm that efficiently generates candidate responses and estimates PE via parameter-sharing conditional neural networks. Experiments across multiple two-player zero-sum games show that Global PSRO achieves lower exploitability and approximates Nash equilibria with significantly fewer policy iterations than prior PSRO methods. The experimental code is available at https://github.com/Zhangjy1997/GlobalPSRO.

Applying machine learning techniques to solving long-standing mathematical conjectures can be particularly challenging due to their extreme reward sparsity. As an illustrative example, we consider Kalai's algebraic Hirsch conjecture and recast the construction of its counterexamples as a sparse-reward reinforcement learning problem on graphs. We propose a constrained options-based HRL framework with an equivariant graph neural network policy, which allows us to learn useful temporal abstractions for this task. We evaluate our approach over a wide range of degrees and demonstrate that it consistently outperforms classical RL algorithms as well as greedy search. By exploiting the hierarchical structure of the problem, we effectively provide a first-of-its-kind application of HRL to a problem in commutative algebra.

Reinforcement learning has advanced video reasoning in large multi-modal models, yet dominant pipelines either rely on on-policy self-exploration, which plateaus at the model’s knowledge boundary, or hybrid replay that mixes policies and demands careful regularization. Dynamic context methods zoom into focused evidence but often require curated pretraining and two-stage tuning, and their context remains bounded by a small model’s capability. In contrast, larger models excel at instruction following and multi-modal understanding, can supply richer context to smaller models, and rapidly zoom in on target regions via simple tools. Building on this capability, we introduce an observation-level intervention: a frozen, tool-integrated teacher identifies the missing spatiotemporal dependency and provides a minimal evidence patch (e.g., timestamps, regions etc.) from the original video while the question remains unchanged. The student answers again with the added context, and training updates with a chosen-rollout scheme integrated into Group Relative Policy Optimization (GRPO). We further propose a Robust Improvement Reward (RIR) that aligns optimization with two goals: outcome validity through correct answers and dependency alignment through rationales that reflect the cited evidence. Advantages are group-normalized across the batch, preserving on-policy exploration while directing it along causally meaningful directions with minimal changes to the training stack. Experiments on various related benchmarks show consistent accuracy gains and strong generalization. Project page is available at https://jethrojames.github.io/FFR/.

A reliable reward model is essential for aligning large language models (LLMs) with human preferences through reinforcement learning from human feedback (RLHF). However, standard reward models are susceptible to spurious features that are not causally related to human labels. This can lead to *reward hacking*, where high predicted reward does not translate into better behavior. In this work, we address this problem from a causal perspective by proposing a factored representation learning framework that decomposes the model’s contextual embedding into (1) causal factors that are sufficient for reward prediction and (2) non-causal factors that capture reward-irrelevant attributes such as length or sycophantic bias. The reward head is then constrained to depend only on the causal component. In addition, we introduce an adversarial head trained to predict reward from the non-causal factors, while applying gradient reversal to discourage them from encoding reward-relevant information. Experiments on both mathematical and dialogue tasks demonstrate that our method learns more robust reward models and consistently improves downstream RLHF performance over state-of-the-art baselines. Analyses on length and sycophantic bias further validate the effectiveness of our method in mitigating reward hacking behaviors.

Latent categorical variables are frequently found in deep learning architectures. They can model actions in discrete reinforcement-learning environments, represent categories in latent-variable models, or express relations in graph neural networks. Despite their widespread use, their discrete nature poses significant challenges to gradient-descent learning algorithms. While a substantial body of work has offered improved gradient estimation techniques, we take a complementary approach. Specifically, we: 1) revisit the ubiquitous *softmax* function and demonstrate its limitations from an information-geometric perspective; 2) replace the *softmax* with the *catnat* function, a function composed by a sequence of hierarchical binary splits; we prove that this choice offers significant advantages to gradient descent due to the resulting diagonal Fisher Information Matrix. A rich set of experiments - including graph structure learning, variational autoencoders, and reinforcement learning - empirically show that the proposed function improves the learning efficiency and yields models characterized by consistently higher test performance. *Catnat* is simple to implement and seamlessly integrates into existing codebases. Moreover, it remains compatible with standard training stabilization techniques and, as such, offers a better alternative to the *softmax* function.

Combinatorial generalization remains a central challenge in Deep Reinforcement Learning (DRL). Classical planning provides a simple yet challenging setting to study this problem through explicit relational descriptions, without requiring learning from perception. In sparse-reward domains, standard RL exploration via real-time search is ineffective, and learning-based planning methods often rely on expert demonstrations, hindsight relabeling, or random walks from the goal state. In contrast, planners rely on best-first search methods such as $\mathrm{A}^\star$ to solve problems from scratch. We propose a self-improving $\mathrm{WA}^\star$ learning framework in combination with a value heuristic represented by a Relational Graph Neural Network: the heuristic guides search, and the resulting search data updates the heuristic via $Q$-learning. This loop yields heuristics that can function as general policies and solve new instances even without search, where DRL otherwise fails, as we show on puzzles such as Sokoban, PushWorld, The Witness, and the 2023 International Planning Competition benchmarks. Notably, we demonstrate strong zero-shot generalization: For example, heuristics trained on Blocksworld instances with fewer than $30$ blocks successfully solve instances with $488$ blocks without search.

This work studies online episodic tabular Markov decision processes (MDPs) with known transitions and develops best-of-both-worlds algorithms that achieve refined data-dependent regret bounds in the adversarial regime and variance-dependent regret bounds in the stochastic regime. We quantify MDP complexity using a first-order quantity and several new data-dependent measures for the adversarial regime, including a second-order quantity and a path-length measure, as well as variance-based measures for the stochastic regime. To adapt to these measures, we develop algorithms based on global optimization and policy optimization, both built on optimistic follow-the-regularized-leader with log-barrier regularization. For global optimization, our algorithms achieve first-order, second-order, and path-length regret bounds in the adversarial regime, and in the stochastic regime, they achieve a variance-aware gap-independent bound and a variance-aware gap-dependent bound that is polylogarithmic in the number of episodes. For policy optimization, our algorithms achieve the same data- and variance-dependent adaptivity, up to a factor of the episode horizon, by exploiting a new optimistic $Q$-function estimator. Finally, we establish regret lower bounds in terms of data-dependent complexity measures for the adversarial regime and a variance measure for the stochastic regime, implying that the regret upper bounds achieved by the global-optimization approach are nearly optimal.

Natural language interfaces can greatly benefit the accessibility and usability of optimization modeling, and recent advances in large language models (LLMs) show promise in automatically translating textual problem descriptions into executable solver formulations. However, a key challenge for existing approaches is to ensure that the inferred formulation correctly implements the intended task, even if it may execute without errors. We introduce VeriSimpl, a solver–LLM framework for robust natural-language-to-optimization formalization. Our approach is based on the idea of simplification-based verification, where the optimization solver is leveraged to generate simplified diagnostic queries about a candidate formulation to allow the LLM to tractably reason about the correctness of the formulation with respect to the task description. We present such simplification strategies along different dimensions with respect to problem constraints and decision variables, which allow the LLM to reason locally under fixed global contexts. Evaluations on a range of optimization benchmarks show how our approach provides consistent improvements in accuracy over existing methods, while also providing a novel high-precision self-verification signal.

Reinforcement Learning from Human Feedback (RLHF) has become the standard for aligning Large Language Models (LLMs), yet its efficacy is bottlenecked by the high cost of acquiring preference data, especially in low-resource and expert domains. To address this, we introduce ActiveUltraFeedback, a modular active learning pipeline that leverages uncertainty estimates to dynamically identify the most informative responses for annotation. Our pipeline facilitates the systematic evaluation of standard response selection methods alongside Double Reverse Thompson Sampling (DRTS) and DeltaUCB, two novel methods prioritizing response pairs with large predicted quality gaps, leveraging recent results showing that such pairs provide good signals for fine-tuning. Our experiments demonstrate that ActiveUltraFeedback yields high-quality datasets that lead to significant improvements in downstream performance, notably achieving comparable or superior results with as little as one-sixth of the annotated data relative to static baselines. Our pipeline is available at https://github.com/lasgroup/ActiveUltraFeedback and our preference datasets at https://huggingface.co/ActiveUltraFeedback.

We present the first high-probability optimal regret bound for a policy optimization technique applied to the problem of stochastic contextual multi-armed bandit (CMAB) with general offline function approximation. Our algorithm is both efficient and achieves an optimal regret bound of $\widetilde{O}(\sqrt{ K|\mathcal{A}|\log|\mathcal{F}|})$, where $K$ is the number of rounds, $\mathcal{A}$ is the set of arms, and $\mathcal{F}$ is the function class used to approximate the losses. Our results bridge the gap between theory and practice, demonstrating that the widely used policy optimization methods for the contextual bandit problem can achieve a rigorously-proved optimal regret bound. We support our theoretical results with an empirical evaluation of our algorithm.

Retrosynthesis prediction aims to infer the reactant molecules based on a given product molecule, which is a fundamental task in chemical synthesis. However, existing methods rely on a static pattern-matching paradigm, which limits their ability to perform effective logical decision-making from chemical data, leading to a black-box process. We propose Retro-Expert, an interpretable retrosynthesis framework that performs collaborative reasoning by combining the complementary strengths of Large Language Models and specialized models via pure reinforcement learning. It outputs natural language explanations grounded in chemical logic through three components: (1) specialized models provide chemical knowledge that is distilled into a high-quality chemical decision space, (2) LLM-driven critical reasoning to generate predictions with an interpretable reasoning path, and (3) knowledge-grounded policy optimization refines the interpretable decision policy. Experiments show that Retro-Expert surpasses both LLM-based and specialized models across different metrics, while generating chemically grounded explanations that enhance chemists' trust in practice. The source code for this paper is available at https://github.com/MagixRab-ll/Retro-Expert

Reinforcement Learning (RL) with rubric-based rewards has recently shown remarkable progress in enhancing general reasoning capabilities of Large Language Models (LLMs), yet still suffers from ineffective exploration confined to current policy distribution. In fact, RL optimization can be viewed as steering the policy toward an ideal distribution that maximizes the rewards, while effective exploration should align efforts with desired target. Leveraging this insight, we propose HeRL, a ****H***indsight ***e***xperience guided ***R***einforcement ***L***earning* framework to bootstrap effective exploration by explicitly *telling LLMs the desired behaviors* specified in rewards. Concretely, HeRL treats failed attempts along with their unmet rubrics as hindsight experience, which serves as in-context guidance for the policy to explore desired responses beyond its current distribution. Additionally, we introduce a bonus reward to incentivize responses with greater potential for improvement under such guidance. HeRL facilitates effective learning from desired high-quality samples without repeated trial-and-error from scratch, yielding a more accurate estimation of the expected gradient theoretically. Extensive experiments across various benchmarks demonstrate that HeRL achieves superior performance gains over baselines, and can further benefit from experience guided self-improvement at test time.

Agentic reinforcement learning has advanced large language models (LLMs) to reason through long chain-of-thought trajectories while interleaving external tool use. Existing approaches assume a fixed inventory of tools, which limits the adaptability of LLM agents to new or evolving toolsets. We present AutoTool, a training framework that equips LLM agents with dynamic tool-selection capabilities throughout their reasoning trajectories. AutoTool employs a dual-phase optimization pipeline: (i) SFT and RL-based trajectory stabilization for coherent reasoning, and (ii) KL-regularized Plackett–Luce Ranking to refine consistent multi-step tool selection. We further build a 200k dataset with explicit tool-selection rationales across 1,000+ tools and 100+ tasks spanning mathematics, science, code generation, and multimodal reasoning. Across ten diverse benchmarks, we train two base models, Qwen3-8B and Qwen2.5-VL-7B, with AutoTool. With fewer parameters, AutoTool consistently outperforms advanced LLM agents and tool-integration methods, yielding average gains of 6.4\% in math \& science reasoning, 4.5\% in search-based QA, 7.7\% in code generation, and 6.9\% in multimodal understanding. In addition, AutoTool exhibits stronger generalization by dynamically leveraging unseen tools from evolving toolsets during inference.

Parameter Sharing (PS) is widely used to improve efficiency in Multi-Agent Reinforcement Learning (MARL), but it can limit behavioral diversity and degrade performance. This limitation stems from gradient conflicts among agents on shared weights, which hinders effective policy learning. To fully characterize this phenomenon, we propose Geometric Gradient Decomposition Analysis that decomposes gradients with respect to weight vector into radial (scale) and tangential (direction) components and uncover a key insight: agents largely agree on directional updates but substantially disagree on scale updates. Consequently, while recent methods split the shared network into agent-specific subnetworks to mitigate conflicts, they also discard shared directional updates, limiting training efficiency. To address this issue, we propose Hyperspherical Parameter Sharing (HPS), which explicitly decouples direction and scale in parameter sharing. Specifically, HPS constrains the shared backbone weights onto a Riemannian manifold(unit hypersphere), enforcing purely directional learning. Building on this, an agent-specific scale generator outputs multiplicative modulation factors to adjust each agent’s scales, thus preserving heterogeneous response magnitudes without disrupting the shared directions. Experiments on SMAC, SMACv2, VMAS and Predator Prey demonstrate that HPS effectively resolves the scale conflict, significantly outperforming state-of-the-art methods.

High-quality kernel is critical for scalable AI systems, and enabling LLMs to generate such code would advance AI development. However, training LLMs for this task requires sufficient data, a robust environment, and the process is often vulnerable to _reward hacking_ and _lazy optimization_. In these cases, models may hack training rewards or prioritize trivial correctness over meaningful speedup. In this paper, we systematically study reinforcement learning (RL) for kernel generation. We first design **KernelGYM**, a robust distributed GPU environment that supports reward hacking check, data collection from multi-turn interactions and long-term RL training. Building on KernelGYM, we investigate effective multi-turn RL methods and identify a biased policy gradient issue caused by self-inclusion in GRPO. To solve this, we propose Turn-level Reinforce-Leave-One-Out (**TRLOO**) to provide unbiased advantage estimation for multi-turn RL. To alleviate lazy optimization, we incorporate mismatch correction for training stability and introduce Profiling-based Rewards (**PR**) and Profiling-based Rejection Sampling (**PRS**) to overcome the issue. The trained model, Dr. Kernel-14B, reach performance competitive with Claude-4.5-Sonnet in Kernelbench. Finally, we study sequential test-time scaling for Dr. Kernel-14B, which even **outperforms** GPT-5 and Claude-4.5-Sonnet in the Kernelbench level-2 subset.

Ensuring the safety of language models (LMs) while maintaining their usefulness remains a critical challenge in AI alignment. Current approaches rely on sequential adversarial training: generating adversarial prompts and fine-tuning LMs to defend against them. We introduce a different paradigm: framing safety alignment as a non-zero-sum game between an Attacker LM and a Defender LM trained jointly via online reinforcement learning. Each LM continuously adapts to the other's evolving strategies, driving iterative improvement. Our method uses a preference-based reward signal derived from pairwise comparisons instead of point-wise scores, providing more robust supervision and potentially reducing reward hacking. Our RL recipe, AdvGame, shifts the Pareto frontier of safety and utility, yielding a Defender LM that is simultaneously more helpful and more resilient to adversarial attacks. In addition, the resulting Attacker LM converges into a strong, general-purpose red-teaming agent that can be directly deployed to probe arbitrary target models. Code at github.com/facebookresearch/advgame.

A digital twin (DT) is a virtual model of a real-world system that can assist decision-making by simulating scenarios induced by different policies. However, typical machine learning-based DTs do not optimise for this use case. We prove that, when model capacity is limited, training DTs to minimise one-step transition errors can produce suboptimal models for ranking sets of policies according to a reward function. We further show that this holds empirically, even with expressive model classes. To address this, we introduce DT$^2$, a decision-targeted DT training paradigm. Firstly, DT$^2$ uses fitted Q-evaluation to estimate values of candidate policies from offline data. A DT is then trained to generate rollouts that preserve pairwise policy rankings derived from these proxy ground-truth values with an architecture-agnostic loss function. We empirically demonstrate the efficacy of our method across a range of settings and architectures. DT$^2$ consistently improves policy ranking and reduces decision regret during policy selection relative to conventional DT training, both for policies used during training and for unseen policies, while maintaining a good level of raw simulation fidelity.