Policy Optimization

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Overview

Policy optimization studies how to update a decision-making rule so it earns higher rewards while meeting constraints such as safety, fairness, or limited data. Common approaches include policy gradients, actor-critic methods, trust regions and mirror descent, as well as policy iteration and newer generative-policy methods. Work spans continuous-control benchmarks such as MuJoCo, offline and multi-agent settings, and language-model training for mathematical reasoning, coding, and tool use, where token-, segment-, or trajectory-level rewards guide updates. A central challenge is balancing effective exploration and sample reuse with stable updates, useful credit assignment, and improvements that carry over from training to deployment.

Latest papers

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224 papers32 papers in the last four weeks, up 52% on the four weeks before. 0.2% of all new papers.

May 11, 2026

Revisiting Policy Gradients for Restricted Policy Classes: Escaping Myopic Local Optima with kk-step Policy Gradients

This work revisits standard policy gradient methods used on restricted policy classes, which are known to get stuck in suboptimal critical points. We identify an important cause for this phenomenon to be that the policy gradient is itself fundamentally myopic, i.e. it only improves the policy based on the one-step QQ-function. In this work, we propose a generalized kk-step policy gradient method that couples the randomness within a kk-step time window and can escape the myopic local optima in MDPs with restricted policy classes. We show this new method is theoretically guaranteed to converge to a solution that is exponentially close in performance to the optimal deterministic policy with respect to kk. Further, we show projected gradient descent and mirror descent with this kk-step policy gradient can achieve this exponential guarantee in O(1T)O(\frac{1}{T}) iterations, despite only assuming smoothness and differentiability of the value function. This will provide near optimal solutions to previously elusive applications like state aggregation and partially observable cooperative multi-agent settings. Moreover, our bounds avoid the ubiquitous distribution mismatch factors ∣∣dμπ∗/dμπ∣∣∞||d_μ^{π^*} / d_μ^π||_\infty and ∣∣dμπ∗/μ∣∣∞||d_μ^{π^*} / μ||_\infty enabling the kk-step policy gradient method to escape suboptimal critical points that emerge from poor exploration in fully observable settings.

Alex DeWeese, Guannan Qu

Department of Electrical and Computer Engineering Carnegie Mellon University Pittsburgh, PA 15213-3890, USA

Policy GradientPolicy OptimizationPolicy Gradient MethodsPolicy Learning
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May 11, 2026

Natural Policy Gradient as Doubly Smoothed Policy Iteration: A Bellman-Operator Framework

In this work, we show that natural policy gradient, a core algorithm in reinforcement learning, admits an exact formulation as a smoothed and averaged form of policy iteration. Specifically, we introduce doubly smoothed policy iteration (DSPI), a Bellman-operator framework in which each policy is obtained by applying a regularized greedy step to a weighted average of past QQ-functions. DSPI includes policy iteration, dual-averaged policy iteration, natural policy gradient, and more general policy dual averaging methods as special cases. Using only monotonicity and contraction of smoothed Bellman operators, we prove distribution-free global geometric convergence of DSPI. Consequently, standard natural policy gradient and policy dual averaging achieve an iteration complexity of O((1−γ)−1log⁡((1−γ)−1ε−1))\mathcal{O}((1-γ)^{-1}\log((1-γ)^{-1}ε^{-1})) for computing an εε-optimal policy, without modifying the MDP, adding regularization beyond the mirror map inherent in the update, or using adaptive, trajectory-dependent stepsizes. For the unregularized greedy case, corresponding to dual-averaged policy iteration, we also prove finite termination. The same Bellman-operator framework further extends to discounted MDPs with linear function approximation and stochastic shortest path problems.

Phalguni Nanda, Zaiwei Chen

Edwardson School of Industrial Engineering, Purdue University

Policy GradientReinforcement LearningNatural Gradient MethodsNatural Policy GradientPolicy OptimizationPolicy Iteration+2
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May 10, 2026

Trust Region Inverse Reinforcement Learning: Explicit Dual Ascent using Local Policy Updates

Inverse reinforcement learning (IRL) is typically formulated as maximizing entropy subject to matching the distribution of expert trajectories. Classical (dual-ascent) IRL guarantees monotonic performance improvement but requires fully solving an RL problem each iteration to compute dual gradients. More recent adversarial methods avoid this cost at the expense of stability and monotonic dual improvement, by directly optimizing the primal problem and using a discriminator to provide rewards. In this work, we bridge the gap between these approaches by enabling monotonic improvement of the reward function and policy without having to fully solve an RL problem at every iteration. Our key theoretical insight is that a trust-region-optimal policy for a reward function update can be globally optimal for a smaller update in the same direction. This smaller update allows us to explicitly optimize the dual objective while only relying on a local search around the current policy. In doing so, our approach avoids the training instabilities of adversarial methods, offers monotonic performance improvement, and learns a reward function in the traditional sense of IRL--one that can be globally optimized to match expert demonstrations. Our proposed algorithm, Trust Region Inverse Reinforcement Learning (TRIRL), outperforms state-of-the-art imitation learning methods across multiple challenging tasks by a factor of 2.4x in terms of aggregate inter-quartile mean, while recovering reward functions that generalize to system dynamics shifts.

Anish Diwan, Davide Tateo, Christopher E. Mower +3

Technical University of Darmstadt · Robotics Institute Germany (RIG) · Lund University +3

Reinforcement LearningPolicy OptimizationImitation LearningTrust Region Policy OptimizationPolicy Learning
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May 9, 2026

Rethinking Ratio-Based Trust Regions for Policy Optimization in Multi-Agent Reinforcement Learning

Centralized training with decentralized execution (CTDE) is a standard framework for cooperative multi-agent policy-gradient reinforcement learning, allowing agents to learn from joint information while acting from local observations. Ratio-based trust-region methods such as Multi-Agent Proximal Policy Optimization (MAPPO) and Multi-Agent Simple Policy Optimization (MASPO) update decentralized actors using per-agent probability ratios weighted by joint advantage estimates. Teammate non-stationarity increases the variance of these advantages, which in turn increases the variance in the local ratio updates. This exposes two method-specific failure modes: MAPPO's additive clipping removes gradients for outlier samples and weakens recovery from policy drift, while MASPO's soft quadratic penalty can allow probability collapse. We introduce Multi-Agent Ratio Symmetry (MARS), a novel policy optimization objective that replaces these additive ratio-based trust-region mechanisms with a multiplicatively symmetric geometric barrier. MARS preserves corrective gradients while assigning unbounded cost as probability ratios approach zero. Across 47 tasks spanning eight multi-agent environments, including novel JAX benchmarks PaxMen and AeroJAX, MARS matches or exceeds MAPPO and MASPO in aggregate environment-level performance. Ablations show that these gains arise from the geometry of the symmetric barrier rather than from flexible trust-region boundaries alone.

Chulabhaya Wijesundara, Andrea Baisero, Zhongheng Li +3

Northeastern University · STR · University of California, Irvine

Multi-Agent System OptimizationPolicy OptimizationCentralized Training with Decentralized ExecutionProximal Policy OptimizationTrust Region Policy OptimizationCooperative MARL+1
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May 9, 2026

Revisiting Mixture Policies in Entropy-Regularized Actor-Critic

Mixture policies theoretically offer greater flexibility than unimodal policies in continuous action reinforcement learning, but the practical benefits of this complexity remain elusive. Mixture policies are notably absent from most state-of-the-art algorithms, raising a fundamental question: Is the added representational overhead useful? We show that increased flexibility can theoretically enhance solution quality and entropy robustness. Yet standard algorithms like SAC do not leverage these advantages. A core issue is the lack of a low-variance reparameterization trick for mixtures, a luxury Gaussian policies enjoy. We propose a marginalized reparameterization (MRP) estimator to address this, proving it offers lower variance than the standard likelihood-ratio (LR) approach. Our experiments across Gym MuJoCo, DeepMind Control Suite, and MetaWorld show that MRP mixture policies significantly outperform their LR ones, and reach parity (sometimes better) with Gaussian counterparts. In addition, we do find several cases where MRP mixture policies exhibit clear empirical advantages. In this paper, we provide a clearer understanding of the trade-offs involved, elevating MRP mixture policies from theoretical curiosity to a practical tool.

Jiamin He, Samuel Neumann, Jincheng Mei +2

University of Alberta & Amii · Google DeepMind · Canada CIFAR AI Chair

RL ControlPolicy OptimizationMaximum Entropy RLSoft Actor-CriticPolicy Learning
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May 9, 2026

A Single Deep Preference-Conditioned Policy for Learning Pareto Coverage Sets

Preference-conditioned multi-objective reinforcement learning aims to learn a single policy that captures trade-offs across preferences, but under nonlinear scalarization the uniqueness and continuity of the preference-to-solution correspondence remain unclear. We study this problem in tabular multi-objective Markov decision processes (MDPs) using smooth Tchebycheff scalarization as a monotone utility. Under mild interior conditions on the preference set, we prove that each preference induces a unique Pareto-optimal return vector and that this vector depends Lipschitz-continuously on the preference, providing a principled foundation for preference sweeping toward dense Pareto-front coverage. To compute these targets, we formulate the problem over occupancy measures and derive Concave Mirror Descent Policy Iteration (CMDPI), which achieves an O(1/k)O(1/k) objective-suboptimality rate. We further show that each update is equivalent to solving a Kullback-Leibler-regularized MDP with the previous policy as reference, yielding a policy-iteration interpretation and finite-iterate policy continuity across preferences. We instantiate the update as a deep actor-critic algorithm preserving previous-policy regularization. On eight MO-Gymnasium tasks, it achieves the best average hypervolume rank among recent baselines and strong expected-utility performance. Continuous-control experiments indicate gains beyond the discrete-action setting.

Akihiro Kubo, Kosuke Nakanishi, Shin Ishii

International Research Center for Neurointelligence, The University of Tokyo, Tokyo, Japan · ATR Neural Information Analysis Laboratories, Kyoto, Japan · Department of Information Science, Kyoto University, Kyoto, Japan

Multi-Objective Reinforcement LearningPolicy OptimizationPolicy LearningMulti-Objective Optimization
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May 9, 2026

Generative Actor-Critic with Soft Bridge Policies

Expressive generative policies such as diffusion and flow models are appealing for maximum-entropy (MaxEnt) online reinforcement learning because of their ability to model multimodal and highly non-Gaussian action distributions. However, training effective soft generative policies faces two obstacles that often arise together. First, marginal action densities are often unavailable, so existing methods typically rely on entropy bounds, heuristic proxies or approximations. Second, iterative shared-parameter samplers raise inference cost and require backpropagation through time over repeated network evaluations, increasing memory cost and potentially destabilizing policy optimization. These obstacles motivate us to seek a generative actor-critic method that exposes a tractable soft objective while generating each action in just one network evaluation. To this end, we propose soft generative actor-critic (SoftGAC), whose actor is a single stochastic feedforward network with internal Gaussian bridge layers. This explicit bridge structure allows us to lift the soft objective to path space, yielding an analytical path-KL regularizer against a high-entropy reference process for both actor improvement and the soft Bellman bootstrap, without estimating the endpoint entropy. Crucially, the actor generates each action in only one network evaluation under a total parameter budget comparable to strong baselines, substantially reducing inference cost relative to the existing iterative diffusion and flow policies. It also avoids long unrolled backpropagation through time. Across challenging continuous-control benchmarks, our method achieves competitive or superior returns compared with strong diffusion and flow policies, demonstrating a clear advantage in the compute-return tradeoff.

Ke He, Le He, Shunpu Tang +2

Guangzhou University · Zhejiang University · Southeast University

Policy OptimizationMaximum Entropy RLContinuous ControlRL for Generative Models
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May 8, 2026

Auto-Rubric as Reward: From Implicit Preferences to Explicit Multimodal Generative Criteria

Aligning multimodal generative models with human preferences demands reward signals that respect the compositional, multi-dimensional structure of human judgment. Prevailing RLHF approaches reduce this structure to scalar or pairwise labels, collapsing nuanced preferences into opaque parametric proxies and exposing vulnerabilities to reward hacking. While recent Rubrics-as-Reward (RaR) methods attempt to recover this structure through explicit criteria, generating rubrics that are simultaneously reliable, scalable, and data-efficient remains an open problem. We introduce Auto-Rubric as Reward (ARR), a framework that reframes reward modeling from implicit weight optimization to explicit, criteria-based decomposition. Before any pairwise comparison, ARR externalizes a VLM's internalized preference knowledge as prompt-specific rubrics, translating holistic intent into independently verifiable quality dimensions. This conversion of implicit preference structure into inspectable, interpretable constraints substantially suppresses evaluation biases including positional bias, enabling both zero-shot deployment and few-shot conditioning on minimal supervision. To extend these gains into generative training, we propose Rubric Policy Optimization (RPO), which distills ARR's structured multi-dimensional evaluation into a robust binary reward, replacing opaque scalar regression with rubric-conditioned preference decisions that stabilize policy gradients. On text-to-image generation and image editing benchmarks, ARR-RPO outperforms pairwise reward models and VLM judges, demonstrating that explicitly externalizing implicit preference knowledge into structured rubrics achieves more reliable, data-efficient multimodal alignment, revealing that the bottleneck is the absence of a factorized interface, not a deficit of knowledge.

Juanxi Tian, Fengyuan Liu, Jiaming Han +6

1Nanyang Technological University · 2Ant Group · 3MMLab, The Chinese University of Hong Kong +1

Policy OptimizationMultimodal Reward ModelingRubric-Based RLMultimodal GenerationRL for Image GenerationRubric-Based Evaluation
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May 8, 2026

Reflective Prompted Policy Optimization: Trajectory-Grounded Revision and Salience Bias

Existing LLM-based policy optimizers see only scalar rewards: that a policy scored 0.45, but not whether the agent got stuck in a loop, fell into a hole on the third step, or performed well on 19 out of 20 rollouts and failed catastrophically on one. We propose Reflective Prompted Policy Optimization (R2PO), a two-stage LLM framework for policy search over compact policy classes that augments scalar reward feedback with trajectory-level behavioral evidence. A Search-LLM proposes candidate policy parameters; the environment executes them; a Critic-LLM inspects the resulting rollouts and proposes targeted revisions grounded in observed states, actions, and rewards. Across ten environments, ablations show R2PO's gains require separating global search from behavior-grounded revision and using selection to filter high-variance edits. We further identify a dominant failure mode, salience bias: when presented with multiple rollouts, the Critic-LLM fixates on improving a single failure even when most trajectories succeed. In a three-trajectory variant where the Critic-LLM sees the best, worst, and median rollout, this behavior explains 76.6% of regressions on CartPole. R2PO mitigates this by reasoning over aggregate rollout statistics, median-trajectory selection, and a revision rule. Using a 20B open-weight model, R2PO achieves the highest mean best reward across all ten environments, reaches near-optimal performance substantially earlier (e.g., near-maximum CartPole reward within ~500 episodes), and trains far more stably than both deep RL and prior LLM-based methods. These results show that treating trajectories as first-class in-context evidence, rather than artifacts reduced to scalar returns, changes how even comparatively small LLMs search over policy spaces, enabling them to learn faster, diagnose more precisely, and reliably improve external controllers.

Rahaf Abu Hara, Vaibbhav Murarri, Claudio Zito

Laboratory of AI and Robotics Research (LAIRR) Heriot-Watt University Dubai, United Arab Emirates

Policy OptimizationLLM-Guided RLPolicy Learning
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May 8, 2026

Drifting Field Policy: A One-Step Generative Policy via Wasserstein Gradient Flow

We propose Drifting Field Policy (DFP), a non-ODE one-step generative policy built on the drifting model paradigm. We frame the policy update as a reverse-KL Wasserstein-2 gradient flow toward a soft target policy, so that each DFP update corresponds to a gradient step in probability space. By construction, this gradient is decomposed into an ascent toward higher action-value regions and a score matching with the anchor policy as a trust region. We further derive a simple, tractable surrogate of the otherwise intractable update loss, akin to behavior cloning on top-K critic-selected actions. We find empirically that this mechanism uniquely benefits the drifting backbone owing to its non-ODE parameterization. With one-step inference, DFP achieves state-of-the-art performance on several manipulation tasks across Robomimic and OGBench, outperforming ODE-based policies.

Juil Koo, Mingue Park, Jiwon Choi +2

KAIST

Robot Policy LearningWasserstein Gradient FlowsPolicy OptimizationRL for Generative ModelsPolicy LearningDrifting Models
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May 8, 2026

Model-Driven Policy Optimization in Differentiable Simulators via Stochastic Exploration

Differentiable planning enables gradient-based optimization of decision-making problems by leveraging differentiable models of system dynamics. However, in highly nonlinear and hybrid discrete-continuous domains, the resulting optimization landscapes are often ill-conditioned, with flat regions and sharp transitions that hinder effective optimization. We propose Model-Driven Policy Optimization (MDPO), a framework that introduces stochastic exploration into differentiable planning by injecting noise into the action space during optimization. Leveraging access to the model, MDPO further adapts the noise magnitude based on gradient-derived sensitivity of the trajectory objective, yielding a time-dependent exploration profile. This enables improved exploration of the objective landscape and helps escape poor local optima via dynamic allocation of exploration across timesteps and iterations. Experiments on benchmark domains demonstrate that MDPO consistently outperforms deterministic differentiable planning, including both the noise-free variant of our method and available state-of-the-art implementations, as well as model-free baselines such as PPO, significantly improving solution quality across challenging nonlinear and hybrid settings. We further analyze the evolution of the adaptive noise magnitude across both time steps and optimization iterations, providing insight into how exploration is allocated during learning.

Yuval Aroosh, Ayal Taitler

Department of Industrial Engineering and Management Ben-Gurion University of the Negev Beer Sheva, Israel

Policy OptimizationRL ExplorationModel-Based Planning
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May 7, 2026

SNAPO: Smooth Neural Adjoint Policy Optimization for Optimal Control via Differentiable Simulation

Many real-world problems require sequential decisions under uncertainty: when to inject or withdraw gas from storage, how to rebalance a pension portfolio each month, what temperature profile to run through a pharmaceutical reactor chain. Dynamic programming solves small instances exactly but scales exponentially in state dimensions. Black-box reinforcement learning handles high-dimensional states but trains slowly and produces no sensitivities. We introduce SNAPO (Smooth Neural Adjoint Policy Optimization), a framework that embeds a neural policy inside a known, differentiable simulator, replaces hard constraints with smooth approximations, and computes exact gradients of the objective with respect to all policy parameters and all inputs in a single adjoint pass. We demonstrate SNAPO on three domains: natural gas storage (training in under a minute, 365 forward curve sensitivities at no additional cost per sensitivity), pension fund asset-liability management (6.5x-200x sensitivity speedup over bump-and-revalue, scaling with the number of risk factors), and pharmaceutical manufacturing (cross-unit sensitivities through a 4-unit process chain, with 20 ICH Q8 regulatory sensitivities from 5 adjoint passes in 74.5 milliseconds). All sensitivities are produced by the same backward pass that trains the policy, at a cost proportional to one reverse pass regardless of how many sensitivities are computed.

Dmitri Goloubentsev, Natalija Karpichina

MatLogica, U.K.

Policy OptimizationDifferentiable ProgrammingDifferentiable OptimizationOptimal Control
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May 7, 2026

Listwise Policy Optimization: Group-based RLVR as Target-Projection on the LLM Response Simplex

Reinforcement learning with verifiable rewards (RLVR) has become a standard approach for large language models (LLMs) post-training to incentivize reasoning capacity. Among existing recipes, group-based policy gradient is prevalent, which samples a group of responses per prompt and updates the policy via group-relative advantage signals. This work reveals that these optimization strategies share a common geometric structure: each implicitly defines a target distribution on the response simplex and projects toward it via first-order approximation. Building on this insight, we propose Listwise Policy Optimization (LPO) to explicitly conduct the target-projection, which demystifies the implicit target by restricting the proximal RL objective to the response simplex, and then projects the policy via exact divergence minimization. This framework provides (i) monotonic improvement on the listwise objective with bounded, zero-sum, and self-correcting projection gradients, and (ii) flexibility in divergence selection with distinct structural properties through the decoupled projection step. On diverse reasoning tasks and LLM backbones, LPO consistently improves training performance over typical policy gradient baselines under matched targets, while intrinsically preserving optimization stability and response diversity.

Yun Qu, Qi Wang, Yixiu Mao +11

Department of Automation, Tsinghua University · 2LLM Department, Tencent

RL for Language Model ReasoningGroup Relative Policy OptimizationPolicy OptimizationReinforcement Learning with Verifiable RewardsRL Post-Training
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May 7, 2026

AGPO: Asymmetric Group Policy Optimization for Verifiable Reasoning and Search Ads Relevance at JD

Reinforcement Learning with Verifiable Rewards (RLVR) has demonstrated notable success in enhancing the reasoning performance of large language models (LLMs). However, recent studies reveal that while current RLVR methods improve sampling efficiency towards correct paths, they do not elicit fundamentally new reasoning patterns. Instead, the reasoning capability boundary of trained models often narrows compared to their base models, with base models achieving higher coverage at large sample sizes. In this work, we propose Asymmetric Group Policy Optimization (AGPO) to counteract this boundary shrinkage. AGPO adopts a negative-dominant reinforcement strategy to suppress incorrect reasoning paths, maintaining the base model's exploration capacity. For positive reinforcement, AGPO adopts a group advantage mechanism, which scales positive updates based on intra-group variance, allowing the model to focus on rare correct paths while suppressing updates from trivial paths. Our experiments on five mathematical benchmarks demonstrate that AGPO achieves state-of-the-art accuracy while consistently improving pass@kk performance at scale. In a large-scale industrial application for search ads relevance optimization, AGPO effectively enhances the quality of the data annotation, leading to substantial performance gains in downstream student models.

Yang Xu, Kun Yao, Yiming Deng +3

Nanjing University, Nanjing, China · Peking University, Beijing, China · JD.com, Beijing, China

RL for Language Model ReasoningPolicy OptimizationMathematical ReasoningReinforcement Learning with Verifiable Rewards
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May 7, 2026

Transformers Provably Implement In-Context Reinforcement Learning with Policy Improvement

We investigate the ability of transformers to perform in-context reinforcement learning (ICRL), where a model must infer and execute learning algorithms from trajectory data without parameter updates. We show that a linear self-attention transformer block can provably implement policy-improvement methods, including semi-gradient SARSA and actor-critic, via explicit parameter constructions. Beyond existence, we design a teacher-mimicking training procedure, analyze its gradient-flow dynamics, and establish the first convergence guarantee in the ICRL literature: under suitable richness conditions on the training MDP distribution, gradient flow converges locally and exponentially to an optimal parameter manifold corresponding to the desired RL update. Empirically, training transformers on randomly generated tabular MDPs confirms these predictions: the learned models recover the parameter structure of our explicit constructions and, when deployed on unseen MDPs, deliver strong in-context control performance. Together, these results illuminate how transformer architectures internalize and execute classical reinforcement learning algorithms in context, bridging mechanistic understanding and training dynamics in ICRL.

Haodong Liang, Lifeng Lai

Department of Electrical and Computer Engineering, University of California, Davis

Reinforcement LearningTransformer-Based RLPolicy OptimizationIn-Context RLPolicy Learning
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May 6, 2026

Approximate Next Policy Sampling: Replacing Conservative Target Policy Updates in Deep RL

We revisit a classic "chicken-and-egg" problem in reinforcement learning: to safely improve a policy, the value function must be accurate on the state-visitation distribution of the updated policy. That distribution over states is unknown and cannot be sampled for the purposes of training the value function. Conservative updates solve this problem, but at the cost of shrinking the policy update. This paper explores an alternative solution, Approximate Next Policy Sampling (ANPS), which addresses the problem by modifying the training distribution rather than constraining the policy update. ANPS is satisfied if the distribution of the training data approximates that of the next policy. To demonstrate the feasibility and efficacy of ANPS, we introduce Stable Value Approximate Policy Iteration (SV-API). SV-API modifies the standard approximate policy iteration loop to hold the target policy fixed while an iteratively updated behavioral policy gathers relevant experience. It only commits to a new policy once a convergence criterion has been met. If certain stability criteria are met, the update is guaranteed to be safe; otherwise, it remains no less safe than standard approximate policy iteration. Applying SV-API to PPO yields Stable Value PPO (SV-PPO), which matches or improves performance on high-dimensional discrete (Atari) and continuous control benchmarks while executing substantially larger target policy updates. These results demonstrate the viability of ANPS as a new solution to this classic challenge in RL.

Dillon Sandhu, Ronald Parr

Department of Computer Science, Duke University, USA

Policy OptimizationPolicy IterationProximal Policy OptimizationSafe RLPolicy Learning
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May 5, 2026

Vanishing L2 regularization for the softmax Multi Armed Bandit

Multi Armed Bandit (MAB) algorithms are a cornerstone of reinforcement learning and have been studied both theoretically and numerically. One of the most commonly used implementation uses a softmax mapping to prescribe the optimal policy and served as the foundation for downstream algorithms, including REINFORCE. Distinct from vanilla approaches, we consider here the L2 regularized softmax policy gradient where a quadratic term is subtracted from the mean reward. Previous studies exploiting convexity failed to identify a suitable theoretical framework to analyze its convergence when the regularization parameter vanishes. We prove here theoretical convergence results and confirm empirically that this regime makes the L2 regularization numerically advantageous on standard benchmarks.

Stefana-Lucia Anita, Gabriel Turinici

CEREMADE, Universit´e Paris Dauphine - PSL, CNRS, Paris, France · ‘Octav Mayer” Institute of Mathematics of the Romanian Academy, Bd. Carol I 8, Ias¸i 700505, Romania

Multi-Armed BanditsPolicy GradientPolicy OptimizationPolicy Gradient MethodsPolicy LearningRegularized RL
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May 4, 2026

Reference-Sampled Boltzmann Projection for KL-Regularized RLVR: Target-Matched Weighted SFT, Finite One-Shot Gaps, and Policy Mirror Descent

Online reinforcement learning with verifiable rewards (RLVR) turns checkable outcomes into a scalable training signal, but it keeps rollout generation, verifier scoring, and reference-policy evaluations on the optimization path. Static weighted supervised fine-tuning (SFT) on precomputed rollouts seems to remove this bottleneck, yet a weighted likelihood is not specified by rewards alone: its sampler and weights induce the policy being fit. This paper identifies the reference-sampled weighted-SFT objective whose induced policy equals the fixed-reference KL-regularized RLVR optimizer. The optimizer is the standard Boltzmann target policy, obtained by exponentially tilting the reference policy by verifier reward. Matching a weighted-SFT induced policy to this target forces density-ratio weights; in the reference-sampled subclass, this reduces uniquely, up to prompt scaling, to the prompt-normalized Boltzmann weight exp⁡(r(x,y)/β)/Z(x)\exp(r(x,y)/β)/Z(x). BOLT, a Boltzmann-Targeted SFT procedure, is the empirical estimator of this projection. The finite one-shot analysis separates the exact stored-support price βlog⁡(1/π∗(SN∣x))β\log(1/π^*(S_N\mid x)) from partition estimation, effective-sample-size variance, generalization, optimization, and approximation errors. This decomposition explains why extra SFT epochs cannot repair missing reference-policy coverage and exposes the temperature--coverage--variance frontier. When coverage needs adaptive sampling, refreshed Boltzmann projections become KL policy mirror descent; finite inner solves enter as additive drift from the exact mirror step. Single-run Qwen experiments provide projection evidence for the target-matched weight, one-shot saturation, refreshed-sampler gains, and optimization-time savings, within the stated single-run scope.

Yao Shu, Chenxing Wei, Hongbin Lin +2

Supervised Fine-TuningReinforcement LearningKL-Regularized RLPolicy OptimizationReinforcement Learning with Verifiable Rewards
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May 2, 2026

Segment-Aligned Policy Optimization for Multi-Modal Reasoning

Existing reinforcement learning approaches for Large Language Models typically perform policy optimization at the granularity of individual tokens or entire response sequences. However, such formulations often misalign with the natural step-wise structure of reasoning processes, leading to suboptimal credit assignment and unstable training in multi-modal reasoning tasks. To bridge this gap, we propose Segment-Aligned Policy Optimization (SAPO), a novel reinforcement learning paradigm that treats coherent reasoning steps, rather than tokens or full sequences as fundamental units of policy update. SAPO introduces a step-wise Markov decision process abstraction over reasoning segments, accompanied by segment-level value estimation, advantage computation, and importance sampling mechanisms that are semantically aligned with reasoning boundaries. Experiments on representative reasoning benchmarks demonstrate that SAPO consistently outperforms token-level and sequence-level policy optimization methods, achieving significant accuracy improvements while exhibiting better training stability and value estimation consistency. Our work underscores the importance of aligning reinforcement learning updates with the intrinsic structure of reasoning, paving the way for more efficient and semantically grounded policy optimization in complex reasoning tasks. Codes and models will be released to ensure full reproducibility.

Lei Gao, Zhuoming Li, Mengxi Jia +4

Fudan University · China Telecom Artificial Intelligence Technology (Beijing) Co., Ltd. · Southeast University +1

RL for Language Model ReasoningPolicy OptimizationMultimodal Reasoning
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May 1, 2026

SAVGO: Learning State-Action Value Geometry with Cosine Similarity for Continuous Control

While representation and similarity learning have improved the sample efficiency of Reinforcement Learning (RL), they are rarely used to shape policy updates directly in the action space. To bridge this gap, a geometry-aware RL algorithm that explicitly incorporates value-based similarity into the policy update, State-Action Value Geometry Optimization (SAVGO), is proposed. In detail, SAVGO learns a joint state-action embedding space in which pairs with similar action-value estimates exhibit high cosine similarity, while dissimilar pairs are mapped to distinct directions. This learned geometry enables the generation of a similarity kernel over candidate actions sampled at each update, allowing policy improvement to be guided directly toward higher-value regions beyond local gradient-based updates. As a result, representation learning, value estimation, and policy optimization are unified within a single geometry-consistent objective, while preserving the scalability of off-policy actor-critic training. The proposed method is evaluated on standard MuJoCo continuous-control benchmarks, demonstrating improvements over strong baselines on challenging high-dimensional tasks. Ablation studies are done to analyze the contributions of value-geometry learning and similarity-based policy updates.

Stavros Orfanoudakis, Pedro P. Vergara

Delft University of Technology, The Netherlands

Representation LearningPolicy OptimizationContinuous ControlActor-Critic Methods
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Apr 26, 2026

SFT-then-RL Outperforms Mixed-Policy Methods for LLM Reasoning

Recent mixed-policy optimization methods for LLM reasoning that interleave or blend supervised and reinforcement learning signals report improvements over the standard SFT-then-RL pipeline. We show that numerous recently published research papers rely on a faulty baseline caused by two distinct bugs: a CPU-offloaded optimizer bug in DeepSpeed that silently drops intermediate micro-batches during gradient accumulation (affecting multiple downstream frameworks including TRL, OpenRLHF and Llama-Factory), and a loss aggregation bug in OpenRLHF that incorrectly weights per-mini-batch losses. Together they suppress SFT performance, with the optimizer bug accounting for most of the gap and the loss aggregation bug contributing a smaller additional effect. Once corrected, the standard SFT-then-RL pipeline surpasses every published mixed-policy method we evaluate by +3.8 points on math benchmarks with Qwen2.5-Math-7B and by +22.2 points with Llama-3.1-8B. Even a truncated variant with just 50 RL steps outperforms mixed-policy methods on math benchmarks while using fewer FLOPs.

Alexis Limozin, Eduard Durech, Torsten Hoefler +2

ETH AI Center, ETH Zürich · EPFL · Allen Institute for AI

RL for Language Model ReasoningPolicy OptimizationLLM Post-TrainingRL Fine-TuningLLM Reasoning
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Apr 23, 2026

Tempered Sequential Monte Carlo for Trajectory and Policy Optimization with Differentiable Dynamics

We propose a sampling-based framework for finite-horizon trajectory and policy optimization under differentiable dynamics by casting controller design as inference. Specifically, we minimize a KL-regularized expected trajectory cost, which yields an optimal "Boltzmann-tilted" distribution over controller parameters that concentrates on low-cost solutions as temperature decreases. To sample efficiently from this sharp, potentially multimodal target, we introduce tempered sequential Monte Carlo (TSMC): an annealing scheme that adaptively reweights and resamples particles along a tempering path from a prior to the target distribution, while using Hamiltonian Monte Carlo rejuvenation to maintain diversity and exploit exact gradients obtained by differentiating through trajectory rollouts. For policy optimization, we extend TSMC via (i) a deterministic empirical approximation of the initial-state distribution and (ii) an extended-space construction that treats rollout randomness as auxiliary variables. Experiments across trajectory- and policy-optimization benchmarks show that TSMC is broadly applicable and compares favorably to state-of-the-art baselines.

Heng Yang

Harvard University

Markov Chain Monte CarloTrajectory OptimizationPolicy Optimization
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Apr 20, 2026

Bounded Ratio Reinforcement Learning

Proximal Policy Optimization (PPO) has become the predominant algorithm for on-policy reinforcement learning due to its scalability and empirical robustness across domains. However, there is a significant disconnect between the underlying foundations of trust region methods and the heuristic clipped objective used in PPO. In this paper, we bridge this gap by introducing the Bounded Ratio Reinforcement Learning (BRRL) framework. We formulate a novel regularized and constrained policy optimization problem and derive its analytical optimal solution. We prove that this solution ensures monotonic performance improvement. To handle parameterized policy classes, we develop a policy optimization algorithm called Bounded Policy Optimization (BPO) that minimizes an advantage-weighted divergence between the policy and the analytic optimal solution from BRRL. We further establish a lower bound on the expected performance of the resulting policy in terms of the BPO loss function. Notably, our framework also provides a new theoretical lens to interpret the success of the PPO loss, and connects trust region policy optimization and the Cross-Entropy Method (CEM). We additionally extend BPO to Group-relative BPO (GBPO) for LLM fine-tuning. Empirical evaluations of BPO across MuJoCo, Atari, and complex IsaacLab environments (e.g., Humanoid locomotion), and of GBPO for LLM fine-tuning tasks, demonstrate that BPO and GBPO generally match or outperform PPO and GRPO in stability and final performance.

Yunke Ao, Le Chen, Bruce D. Lee +5

ETH Zurich · MPI for Intelligent Systems · University of Alberta +2

Reinforcement LearningGroup Relative Policy OptimizationPolicy OptimizationProximal Policy OptimizationTrust Region Policy OptimizationRL Fine-Tuning+1
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Apr 20, 2026

StepPO: Step-Aligned Policy Optimization for Agentic Reinforcement Learning

Agentic reinforcement learning (RL) is emerging as a critical post-training paradigm for improving LLM agent capabilities. Existing RL algorithms for LLMs largely follow the token-centric paradigm as in RLHF and RLVR, where tokens serve as the basic units for modeling and optimization. However, this paradigm introduces a granularity mismatch in agentic RL, as it optimizes token-level predictions while LLM agents make step-level decisions through cycles of environmental observations and actions. To bridge this gap, we propose StepPO, a step-centric paradigm for agentic RL via step-aligned policy optimization. Specifically, we reformulate agentic RL from a token-level Markov Decision Process (MDP) into a step-level MDP, where interaction steps serve as the basic trajectory representations. We further propose step-level credit assignment to align policy optimization with the natural granularity of agent decisions. Together, StepPO optimizes agent policies at the step level for multi-turn agent-environment interaction. Experiments across multi-hop QA, academic paper search, and text-world action tasks show that StepPO consistently outperforms various RL algorithms. Further analyses provide insights into how step-centric paradigm improves agent training. We hope this step-centric paradigm offers a useful lens for understanding agent behavior and a practical path for training more capable LLM agents.

Daoyu Wang, Qingchuan Li, Mingyue Cheng +4

State Key Laboratory of Cognitive Intelligence, University of Science and Technology of China

Agentic RLCredit Assignment in RLPolicy OptimizationStep-Level Credit AssignmentRL for LLM Agents
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Apr 20, 2026

OmniVLA-RL: A Vision-Language-Action Model with Spatial Understanding and Online RL

Visual-Language-Action (VLA) models represent a paradigm shift in embodied AI, yet existing frameworks often struggle with imprecise spatial perception, suboptimal multimodal fusion, and instability in reinforcement learning. To bridge these gaps, we propose OmniVLA-RL, a novel architecture that leverages a Mix-of-Transformers (MoT) design to synergistically integrate reasoning, spatial, and action experts. Furthermore, we introduce Flow-GSPO, which reformulates flow matching as a Stochastic Differential Equation (SDE) process and integrates it with Group Segmented Policy Optimization (GSPO) to enhance action precision and training robustness. Extensive evaluations on the LIBERO and LIBERO-Plus benchmarks demonstrate that OmniVLA-RL achieves decent overall performance and surpasses mainstream existing methods, effectively overcoming the fundamental limitations of current VLA models.

Haoxiang Jie, Yaoyuan Yan, Xiangyu Wei +4

1AI Lab, Country Garden Services · 3VBot · 2Omni AI +1

Flow MatchingPolicy OptimizationRoboticsVision-Language-Action Models
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Apr 16, 2026

Beyond Importance Sampling: Rejection-Gated Policy Optimization

We propose a new perspective on policy optimization: rather than reweighting all samples by their importance ratios, an optimizer should select which samples are trustworthy enough to drive a policy update. Building on this view, we introduce Rejection-Gated Policy Optimization (RGPO), which replaces the importance sampling ratio r_theta = pi_theta / pi_old with a smooth, differentiable acceptance gate alpha_theta(s, a) = g(r_theta(s, a)) in the range [0, 1]. Unlike prior work that applies rejection sampling as a data-level heuristic before training, RGPO elevates rejection to an optimization principle: the gate participates directly in gradient computation and is implicitly updated alongside the policy. RGPO provides a unified framework: the policy gradients of TRPO, PPO, and REINFORCE all correspond to specific choices of the effective gradient weight w(r) = g'(r) * r. We prove that RGPO guarantees finite, bounded gradient variance even when importance sampling ratios are heavy-tailed (where IS variance diverges). We further show that RGPO incurs only a bounded, controllable bias and provides an approximate monotonic policy improvement guarantee analogous to TRPO. RGPO matches PPO in computational cost, requires no second-order optimization, and extends naturally to RLHF-style preference alignment. In online preference fine-tuning of Qwen2.5-1.5B-Instruct on Anthropic HH-RLHF (n = 3 seeds), RGPO uses a dual-ratio gate that anchors learning to both the previous policy and the reference model, achieving a Pareto-dominant outcome: the highest reward among online RL methods (+14.8% vs. PPO-RLHF) and the lowest KL divergence to the reference model (-16.0% vs. PPO-RLHF, -53.1% vs. GRPO).

Ziwu Sun, Zhen Gao, Jiyong Zhang +1

Importance SamplingPolicy OptimizationPolicy Gradient MethodsRL Fine-TuningPolicy LearningImportance Sampling for RL
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Apr 16, 2026

Wasserstein Formulation of Reinforcement Learning. An Optimal Transport Perspective on Policy Optimization

We present a geometric framework for Reinforcement Learning (RL) that views policies as maps into the Wasserstein space of action probabilities. First, we define a Riemannian structure induced by stationary distributions, providing rigorous guarantees for their existence in a general context. We then define the tangent space of policies and characterize the geodesics, specifically addressing the measurability of vector fields mapping from the state space to the tangent space of probability measures over the action space. Next, we formulate a general RL optimization problem and construct a gradient flow using Otto's calculus. We compute the gradient and the Hessian of the energy (i.e., the expected cumulative cost), providing a formal second-order analysis. Finally, we illustrate the method with numerical examples: we compute the gradient directly from our theoretical formalism for low-dimensional problems, and we illustrate the numerical applicability of our formal framework to high-dimensional continuous control by parameterizing the policy with a neural network optimized via an ergodic approximation of the cost.

Mathias Dus

IRMA

Reinforcement LearningWasserstein Gradient FlowsPolicy Optimization
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Apr 15, 2026

Positive-Only Drifting Policy Optimization

In the field of online reinforcement learning (RL), traditional Gaussian policies and flow-based methods are often constrained by their unimodal expressiveness, complex gradient clipping, or stringent trust-region requirements. Moreover, they all rely on post-hoc penalization of negative samples to correct erroneous actions. This paper introduces Positive-Only Drifting Policy Optimization (PODPO), a likelihood-free and gradient-clipping-free generative approach for online RL. By leveraging the drifting model, PODPO performs policy updates via advantage-weighted local contrastive drifting. Relying solely on positive-advantage samples, it elegantly steers actions toward high-return regions while exploiting the inherent local smoothness of the generative model to enable proactive error prevention. In doing so, PODPO opens a promising new pathway for generative policy learning in online settings.

Qi Zhang

Policy OptimizationRL for Generative Models
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Apr 14, 2026

Token-Level Policy Optimization: Linking Group-Level Rewards to Token-Level Aggregation via Sequence-Level Likelihood

Group Relative Policy Optimization (GRPO) has significantly advanced the reasoning ability of large language models (LLMs), particularly in their mathemat ical reasoning performance. However, GRPO and related entropy regularization methods still struggle with token-level sparse-rewards, which is an inherent chal lenge in chain-of-thought (CoT) reasoning. These approaches often rely on undifferen tiated token-level entropy regularization, which easily leads to entropy collapse or model degradation under sparse token rewards. In this work, we propose TEPO, a novel token-level framework that (1) leverages sequence-level likelihood to link group-level rewards with individual tokens via token-level aggregation, and (2) introduces a token-level KL-Divergence mask constraint that targets tokens with positive advantages and decreasing entropy to mitigate abrupt policy updates. Experiments demonstrate that TEPO not only achieves state-of-the-art performance on mathematical reasoning benchmarks but also markedly enhances training stability, reducing convergence time by 50% compared with GRPO/DAPO.

Xingyu Lin, Yilin Wen, Du Su +5

College of Computer Science and Technology, Jilin University · Key Laboratory of Symbolic Computation and Knowledge Engineering of MOE, Jilin University · Baidu Inc. +2

RL for Language Model ReasoningPolicy OptimizationLLM ReasoningSparse-Reward RL
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Apr 13, 2026

Olfactory pursuit: catching a moving odor source in complex flows

Locating and intercepting a moving target from possibly delayed, intermittent sensory signals is a paradigmatic problem in decision-making under uncertainty, and a fundamental challenge for, e.g., animals seeking prey or mates and autonomous robotic systems. Odor signals are intermittent, strongly mixed by turbulent-like transport, and typically lag behind the true target position, thereby complicating localization. Here, we formulate olfactory pursuit as a partially observable Markov decision process in which an agent maintains a joint belief over the target's position and velocity. Using a discrete run-and-tumble model, we compute quasi-optimal policies by numerically solving the Bellman equation and benchmark them against well-established information-theoretic strategies such as Infotaxis. We show that purely exploratory policies are near-optimal when the target frequently reorients, but fail dramatically when the target exhibits persistent motion. We thus introduce a computationally efficient hybrid policy that combines the information-gain drive of Infotaxis with a "greedy" value function derived from an associated fully observable control problem. Our heuristic achieves near-optimal performance across all persistence times and substantially outperforms purely exploratory approaches. Moreover, our proposal demonstrates strong robustness even in more complex search scenarios, including continuous run-and-tumble prey motion with moderate persistence time, model mismatch, and more accurate plume dynamics representation. Our results identify predictive inference of target motion as the key ingredient for effective olfactory pursuit and provide a general framework for search in information-poor, dynamically evolving environments.

Maurizio Carbone, Lorenzo Piro, Robin A. Heinonen +3

Istituto dei Sistemi Complessi, CNR, Via dei Taurini 19, 00185 Rome, Italy and INFN “Tor Vergata", Via della Ricerca Scientifica 1, 00133 Rome, Italy · Department of Physics & INFN, Tor Vergata University of Rome, Via della Ricerca Scientifica 1, 00133 Rome, Italy · Machine Learning Genoa Center (MaLGa) & Department of Civil, Chemical and Environmental Engineering, University of Genoa, Genoa, Italy +2

Policy OptimizationPartially Observable Markov Decision Processes
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