Policy Gradient Methods

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7 papers in the last four weeks, up 133% on the four weeks before. 0.1% of all new papers.

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Latest papers 108

Oct 8, 2026math.OC

Randomized Transport Maps for Model-Free Policy-Gradient Mean-Field Control

We develop a model-free policy gradient method for discrete-time mean-field control (MFC). In MFC, the policy affects the objective both through the controlled dynamics and through the population distribution. Standard REINFORCE estimators capture the first effect but not the second. We introduce Transport REINFORCE, a transport map-based approach that perturbs a suitable transformation of the population distribution to estimate this missing mean-field contribution. The method applies to both finite and continuous state spaces. In finite state spaces, we perturb the population distribution directly on the probability simplex through a convex combination of the current population weights and random weights. In continuous state spaces, we project the population distribution onto the manifold of Gaussian mixtures, and then randomize it via a transport map that ensures the perturbed law remains within this manifold. We prove consistency of the perturbed objective and gradient as the perturbation vanishes, and derive bias and mean-square error bounds for the resulting sample-based gradient estimator. Numerical experiments on several MFC benchmarks show that Transport REINFORCE improves over standard REINFORCE.

Adonis Jamal, Samy Mekkaoui, Yadh Hafsi +1

École Polytechnique

Policy Gradient Methods Model-Free RL

Oct 7, 2026cs.LG

Temporally Interpretable Differentiable Decision Trees

Interpretability offers a solution to safe autonomy by providing transparency into an agent's underlying decision-making model. Within sequential-decision making tasks, differentiable decision trees (DDTs) are one approach to such interpretability, maintaining automatic-differentiable policies while providing humans with a discrete tree-based visualization. Nonetheless, current implementations of DDTs are not well-suited for sequential-decision making domains, as there exists an inherent mismatch between a tree's single-timestep behavior and a human's multi-timestep planning. Our work thus introduces time as a new dimension of interpretability, coined as temporal interpretability, and demonstrates how temporal abstractions via action chunking improve it. We achieve this by first introducing two novel policy gradient algorithms that incorporate action chunking. Additionally, to maintain parameter-efficient trees, we develop an information-theoretic tree restructuring algorithm that modifies the tree during training. Across four simulation environments, we find that warm-starting action chunked DDTs from a distilled action chunked policy is the most effective way to obtain temporally interpretable trees: they match neural network policies in three of the four domains while using up to 80

\%

fewer parameters. Our code is available at https://github.com/ei5uke/temp-interp.

Eisuke Hirota, Aarav Sane, Rohan Paleja

Department of Computer Science, Purdue University · Thomas Lord Department of Computer Science, University of Southern California

Interpretable ML Interpretability in RL Reinforcement Learning Policy Gradient Methods

Oct 7, 2026cs.LG

A Closed-Loop Non-Asymptotic Convergence Analysis of PPO with Learned Critics and Clipping

Despite its widespread use, Proximal Policy Optimization with clipping (PPO-Clip) remains difficult to tune, and the interactions among critic learning, clipping, and rollout reuse remain incompletely understood. We develop a \emph{non-asymptotic} analysis of PPO-Clip as a \emph{closed-loop actor--critic} system. It captures actor--critic coupling, nonsmooth probability-ratio clipping, finite-batch reuse, and predictable early stopping under explicit coverage and critic regularity assumptions, using raw GAE and Monte Carlo critic targets. Our synchronous and asynchronous guarantees jointly characterize policy stationarity and the tracking accuracy of the learned critic, with explicit dependence on algorithmic parameters. A sufficient coupling condition gives optimization, critic tracking, clipping, and finite-batch errors a common amplification bound. The asynchronous result also requires a delay-dependent critic stepsize restriction; violating these conditions does not establish divergence. For finite layered MDPs with tabular critics, a uniform bound on the actual clipped-gradient class replaces complete-trajectory counting. A verified growing-horizon family has polynomial sample complexity, and a two-time-scale schedule gives

O(T^{-2/5})

stationarity and critic-tracking bounds with explicit fresh-rollout accounting. These results together advance our understanding about PPO and provide theoretical guidance in tuning.

Junwei Su, Mengfan Liu, Yanyong Zhang +1

School of Artificial Intelligence and Data Science, University of Science and Technology of China · Department of Computer Science, University of Hong Kong

Proximal Policy Optimization Actor-Critic Methods Policy Gradient Methods Sample-Efficient RL Asynchronous RL

Oct 6, 2026cs.LG

Convex-Concave Reinforcement Learning

Policy learning drives many of the most consequential and heavily-invested applications of reinforcement learning today. Yet the core optimization problem it rests on (maximizing expected return) is notoriously non-convex, even under a direct policy parameterization, and the field has largely responded by avoiding it: optimizing convex surrogate approximations of the return under trust-region constraints (NPG, TRPO, PPO, AWR). We show that this seemingly unstructured problem is not actually structureless. In log-density-ratio coordinates

y := \log[π/π_n]

, the exact per-iteration objective, computable via per-decision importance sampling (PDIS), is a difference-of-convex-constrained difference-of-convex (DC-constrained DC) program. This structure lets us move beyond surrogate approximations: it recovers CPI, NPG, TRPO, and AWR as special cases along interpretable axes, and it opens a multi-step axis

k

that couples consecutive decisions. We solve the per-iteration program with sequential convex programming (SCP), the standard solver for difference-of-convex problems, and give convergence guarantees under mild conditions, bridging the difference-of-convex optimization and RL literatures. Empirically, multi-step Convex-Concave RL (CCRL) wins on diagnostic MDPs where credit must propagate across a horizon (its advantage growing with the dependency length), is competitive with a tuned PPO on classic control, and on a realistic, stochastic, mid-horizon healthcare domain converges markedly faster than tuned PPO to the same near-optimal survival, with an 11.3% higher area under the training curve.

Shripad V. Deshmukh, Yaswanth Chittepu, Dhawal Gupta +2

University of Massachusetts · Institute of Foundation Models

Reinforcement Learning Policy Gradient Methods Nonconvex Optimization Step-Level Credit Assignment in RL

Sep 30, 2026cs.CL

OPTS-TTPO: Enhancing Finite-Sample Policy-Gradient Learning with Tree Search

The policy-gradient theorem gives the exact gradient under the current policy, but finite on-policy samples may miss rare high-return trajectories. We study whether tree search improves their coverage within a fixed budget while controlling gradient bias. We introduce On-Policy Parallel Tree Search (OPTS) and Tree Trajectory Policy Optimization (TTPO) using on-policy tree trajectories, which sample new suffixes from the current policy at visited states. This needs no action-distribution correction, although branching changes state visitation. Our Branch Aggregation Lemma shows that branch-weighted tree statistics recover chain expectations when branch choices and weights are fixed before outgoing transitions are sampled. OPTS selects expansion states using estimated performance differences. Under deterministic dynamics, exact values, and max-backup advantages, the induced search policy's expected return improves monotonically with the budget. We bound the gradient bias from adaptive expansion and show that max backup assigns prefix credit to actions leading to better discovered suffixes. Against a finite chain reference, TTPG's measured bias stays near its no-branching level, while NaivePG's bias grows from 0.1251 to 0.4884. At matched budgets, reward- and value-guided OPTS improve correct-answer coverage and majority-vote accuracy over independent sampling. At matched branch counts, OPTS + TTPG gains coverage with a modest bias increase relative to Fixed-branch + TTPG. Under matched interaction or rollout budgets, OPTS-TTPO improves MuJoCo tail returns over PPO by up to 28.6%, achieves a 34-22-1 win-loss-tie record against PPO on Atari-57 under the last-100-log mean-return metric, and improves micro-averaged avg@32 and pass@32 over PPO across all four Qwen3 models.

Junyu Lu, Shichao Weng, Zhiqiang Wang +10

Dobot Robotics · Independent Researcher · Zhejiang University +2

Tree Search Policy Gradient Methods Policy Learning Sample-Efficient RL

Sep 29, 2026cs.MA

Regularized policy gradient with learned mixtures of Gaussians for games with continuous actions

Most successes of superhuman game-playing algorithms are in games with discrete actions, yet in auctions, robotics, sports, or trading, actions are nearly continuous. Prior techniques either rely on expert-designed discretizations or are sample inefficient. We present a scalable policy-gradient algorithm for large sequential games with continuous or mixed discrete and continuous actions. It combines magnetic mirror descent with a mixture of Gaussians reparametrization, trained via self-play. We show that it approximates equilibrium in games where gradient descent fails. In sequential games, it outperforms neural fictitious self-play and matches or outperforms the final strategies of policy space response oracles with 3.5--5.5

\times

fewer samples. In heads-up no-limit Texas hold'em, it performs on par with Slumbot.

Ondřej Kubíček, Viliam Lisý, Tuomas Sandholm

Czech Technical University in Prague · Carnegie Mellon University · Artificial Intelligence Center

Game-Playing Agents Self-Play RL Policy Optimization Policy Gradient Methods Policy Learning Multi-Agent Reinforcement Learning

Sep 28, 2026cs.LG

ORPG: Reconciling Multiple Reward Objectives through Objective-wise Policy Gradients

Multi-reward policy optimization requires a joint update that reflects both the learning signals and the intended relationships among objectives. We introduce Objective-wise Reconciled Policy Gradient (ORPG), which constructs a separate clipped policy objective for each reward and reconciles the resulting gradients into one policy update. For compatible gradients, a cosine-dependent interpolation coordinates their contributions through a partially normalized reference while preserving the norm of their sum. We characterize this update as the unique solution of a spherical directional compromise. For conflicting gradients, projection follows the task's priorities. We evaluate the same compatible rule in helpfulness--safety alignment and correctness--cost optimization for mathematical reasoning. ORPG substantially improves average Useful and Harmless scores over the strongest external baseline on each axis. In mathematics, it achieves the highest average full-budget accuracy and three-budget hypervolume among the compared methods, with more accurate and shorter responses than the initial policy. Component comparisons and training dynamics show the larger contribution of compatible coordination and a complementary benefit from conflict handling. These results support gradient reconciliation for objectives with equal standing and for objectives with an explicit priority.

Shicheng Fang, Yiwen Zhao, Wenbo Tian +4

Fudan University · Shanghai Innovation Institute

Multi-Objective Reinforcement Learning Gradient Interference Policy Gradient Methods

Sep 28, 2026cs.RO

Sufficiency of Zeroth-Order Reward Shaping for Policy Gradient in Stabilization Control

Reward shaping is fundamental to modern robotic control with deep reinforcement learning (RL), yet practitioners still rely heavily on heuristic principles borrowed from classical optimal control and trajectory optimization. Existing methods rarely distinguish reward terms that are intrinsic to the control objective from numerical regularizers, leading to brittle hyperparameter tuning. To determine which quantities a reward must contain, we study the stabilization control problem with a focus on zeroth-order (configuration) and first-order (velocity) information. We theoretically and empirically demonstrate that policy gradient methods can successfully solve stabilization tasks without first-order reward terms, adding such terms can instead introduce severe sensitivity as their scale grows. Conversely, our findings confirm that reward functions must be zeroth-order complete over goal-relevant coordinates, while the first-order state remains necessary in the policy observation under our low-dissipation assumptions. Overall, these results provide actionable and principled guidance for reward design in robotic RL.

Yisheng Zhang, Tao Wang, Sicun Gao

University of California San Diego, La Jolla, CA, USA · Tsinghua University, Beijing, China

Reward Shaping Robotic RL Feedback Control Policy Gradient Methods Reward Design for RL

Sep 27, 2026cs.AI

OSCC: Certified Observation-Safe Coupling Optimization for Gradient-Noise Control in Imperfect-Information Learning

Coupled rollouts can reduce the noise of counterfactual action comparisons, but two issues prevent standard common-random-number constructions from serving as a general learning primitive in imperfect-information environments. First, an invalid coupling may expose hidden state, synchronize endogenous policy randomness, or misalign chance events after counterfactual histories diverge. Second, in multi-action policy optimization, lower return-contrast variance is not by itself the relevant objective: the optimizer depends on the return covariance matrix after projection through the local policy-gradient geometry. We introduce observation-safe counterfactual coupling (OSCC), a framework that defines an admissible class through marginal preservation, information-state safety, branch-local policy randomness, semantic event alignment, and trace-before-oracle replay. We derive a gradient-aware coupling criterion showing that, for marginal-preserving couplings, policy-gradient noise changes are determined by policy-Jacobian-weighted off-diagonal return covariance. This motivates OSCC-Select, a calibration-only selector that chooses among independent, root-only, continuation-only, and fully coupled rollouts using separate safety and gain certificates. Its gain target combines projected gradient noise with measured physical sampling cost and falls back to independent sampling whenever a simultaneous lower confidence bound does not certify improvement. On 100,000 fixed-root Leduc comparisons, the fully coupled CP-GRPO instantiation reduces return-contrast variance from 41.1158 to 18.1441, a 55.87% reduction, while preserving the declared branch marginals. With three actions, OSCC-Select chooses continuation coupling and attains gradient-noise trace 0.0783 versus 0.0917 for return-variance selection. Increasing calibration from 64 to 2,048 groups raises certification from 0.327 to 0.995.

Miaobo Hu, Shuhao Hu, Xiaobo Guo +5

School of Artificial Intelligence, University of Chinese Academy of Sciences, Beijing, China · Institute of Information Engineering, Chinese Academy of Sciences, Beijing, China

Partially Observable RL Policy Gradient Methods Variance Reduction Counterfactual Learning

Sep 21, 2026cs.LG

Luck Is Not Skill: When Do Paired Rollouts Help Group-Relative RL of LLM Agents?

Group-relative reinforcement learning compares rollouts of the same prompt, but independent environment noise can obscure these comparisons. We study paired rollouts, which share an event-keyed noise schedule within each group while preserving each rollout's marginal distribution. Pairing removes the between-schedule component of reward-contrast variance, but need not reduce gradient variance. For one-sided grader noise, we derive an exact condition for reduction and give a counterexample in which reward contrasts improve while gradient variance increases. A controlled study trains a 2B tool-use agent under tool faults and grader flips, with three seeds per design. The protocol was registered with a disclosed, previously completed pilot. Under tool faults, pairing improves final noisy-test success by +5.1 percentage points on average, with all three seed differences positive, but misses the registered learning-curve criterion. The criterion is also missed under grader flips: the validation-AUC difference is +0.003 (95% interval [-0.029, +0.033]). A gradient probe on eight distinct checkpoints from two fault-trained trajectories finds lower mean-centered covariance traces under both noise types: 21 to 30% for grader flips and 40 to 63% for tool faults. These finite-sample measurements support the variance mechanism without establishing a general learning-speed benefit. The results distinguish improving reward comparisons, reducing estimator variance, and improving learning.

Nazmus Sakib

BRAC University, Dhaka, Bangladesh

Group Relative Policy Optimization Policy Gradient Methods RL for LLM Agents

Sep 17, 2026cs.LG

Continuous Delayed-Memory Stochastic Gradient Descent and Continuous-Time Reinforcement Learning from History of Astrophysical Time Series Studies

Quasars are luminous objects in the universe that exhibit stochastic brightness variations encoding information about the supermassive black holes powering them, and modeling these variations from ground-based survey data time series, known as light curves, is a statistical challenge. This paper reviews how stochastic differential equations (SDEs) have been adapted with neural network parameterizations to overcome this challenge in history. We create the Continuous-Delayed-Memory Stochastic Gradient Descent which depend on the past state of the discrete iteration process. We performed the simulation on some 2-dimensional landscape and observed some wider-exploration and more precise convergent behavior compared to Vanilla SGD by adjusting hyperparameters. Besides, we proposed a reinforcement learning structure with continuous time policy gradients for exploratory policies without solving HJB PDE, and we show that its optimality conditions recover the Gibbs policy of previous works.

Juncheng Yi

Continuous-Time RL Policy Gradient Methods Stochastic Gradient Descent

Aug 14, 2026cs.LG

Designing Reinforcement Learning for Diffusion Models: A Unified Path-Space View

Reinforcement learning (RL) post-training provides a direct way to align diffusion models with human preferences and task-specific rewards. However, current RL algorithms for diffusion models remain fragmented: reverse-trajectory methods rely on discretized likelihood ratios, whereas forward-matching methods train on reward-labeled noising versions of the rollout samples. This paper shows that these seemingly different losses arise from a single path-space principle. Starting from the regularized diffusion-RL objective, we use importance sampling between sampling SDEs to obtain an explicit policy-gradient estimator on trajectory space. The estimator contains the stochastic Itô integral underlying Flow-GRPO-type updates; we derive an equivalent variance-reduced value-gradient form that recovers the forward-matching structure of AWM and DiffusionNFT. This identifies the empirical gap between these method families as a variance-reduction effect rather than a difference in RL principle. The derivation yields a unified design space organized by value-gradient estimation, weight functions, and sampling choices. Within this space, we propose a multi-sample KDE value-gradient estimator that reuses rollout groups, together with scale-bounded weight families that retain stable existing recipes while excluding singular ones. Experiments on SD3.5-M and Qwen-Image models validate the variance-reduction explanation and show that the resulting recipe improves over prior diffusion-RL baselines.

Yixian Xu, Yuanrui Zhang, Shengjie Luo +2

State Key Laboratory of General Artificial Intelligence, School of Intelligence Science and Technology, Peking University · ByteDance Seed

Diffusion Model Alignment Policy Gradient Methods RL for Diffusion Models Variance Reduction

Aug 13, 2026cs.LG

The Time Value of Evolution

In evolutionary search, a weak child can be a valuable ancestor that makes high-fitness regions reachable. Immediate-return control is blind to this delayed utility, penalizing mutations through their immediate offspring even when they open productive future lineages. We formalize this hidden dynamic as the time value of evolution within a finite-horizon Markov decision process. To exploit it, we introduce Lineage-Value Policy Gradients (LVPG), a long-horizon actor-critic framework for automated trading policy discovery. Our architecture decouples search control into specialized policy heads over a shared generative backbone: a bootstrapped critic head estimates the value of finite-horizon lineage potential from multi-step mutation trees, while an actor head dynamically modulates mutation intensity over the remaining search budget. We isolate the impact of long-horizon credit assignment against immediate-return optimization across 90 paired runs under matched operators, lineage supervision, folds, seeds, and budgets. Path-based credit assignment substantially accelerates finite-budget search, increasing validation best-so-far AUC by 0.394 Sharpe units. LVPG also produces fewer temporary regressions than immediate-return optimization and recovers from them more often. Finite-horizon lineage value yields more selective non-monotonic search and stronger policies within identical resource constraints.

Matthew Siper, Ahmed Khalifa, Julian Togelius

Nof1, New York University · Nof1, University of Malta

Evolutionary Optimization Policy Gradient Methods Credit Assignment Actor-Critic Methods

Aug 10, 2026cs.LG

Boundary-Seeking Policy Gradient for Safe Reinforcement Learning

Safe reinforcement learning maximizes reward subject to safety constraints. For Constrained Markov Decision Processes, the linear-programming view over occupancy measures implies that whenever the constraint is active at optimality, the optimal policy lies exactly on the constraint boundary, yet standard gradient-based methods do not exploit this structure and often settle in the feasible interior. We introduce Boundary-Seeking Policy Gradient (BSPG), a first-order method whose update combines a tangential component that improves reward while preserving cost to first order with a signed, residual-driven normal component that regulates the policy toward the active boundary from either side; the combined direction admits an algebraic Lagrangian form with an induced coefficient and no learned dual variable. Under exact gradients and stated regularity conditions, the constraint residual converges to zero from either side with a finite-horizon

O(1/\sqrt{T})

bound, the tangential component is a reward-ascent direction on the boundary, and any convergent parameter sequence is stationary on the active constraint set, satisfying the KKT conditions when the limit is also a local maximizer over the feasible set. This complements existing analyses, which certify feasibility but do not characterize the constraint value at convergence. On a standard Safety-Gymnasium navigation task, BSPG attains higher reward while tracking the boundary more tightly than the compared baselines.

Chenhua Fan, Jiahui Zhu, Yuhang Zhang +1

School of EECS, Washington State University, Pullman, WA 99163, USA

Markov Decision Processes Constrained RL Policy Gradient Methods Constrained Optimization Safe RL Policy Learning

Aug 7, 2026math.OC

Wasserstein Policy Gradient for Entropy-Regularized Linear-Quadratic Control

Wasserstein policy gradient (WPG) updates state-conditional action laws by transport in the action space. We study entropy-regularized discounted linear-quadratic (LQ) control. A Bellman verification argument shows that the unrestricted problem has a linear-Gaussian optimal policy, and the discounted-occupancy-weighted statewise Wasserstein gradient is tangent to this policy class. WPG therefore reduces exactly to a finite-dimensional ODE for the feedback gain and action covariance. We prove that this ODE is globally well posed and converges exponentially from every admissible initialization. For each fixed LQ problem, the exponent has a positive limit as the entropy temperature tends to zero and contains no perturbative factor of the form

\exp(-c/τ)

, while retaining the usual dependence on the conditioning of the control problem.

Zhaoyu Zhu, Rui Gao, Shuang Li

University of Illinois Urbana-Champaign · The University of Texas at Austin · The Chinese University of Hong Kong, Shenzhen

Maximum Entropy RL Policy Gradient Methods Linear Quadratic Regulator

Aug 6, 2026cs.LG

LC-GRPO: Bridging Train-Inference Gap for Flow-Based GRPO with Langevin Correction

Flow-based generative models are typically sampled by solving a deterministic ordinary differential equation (ODE), whereas online reinforcement learning requires stochastic rollouts for policy exploration and optimization. Existing GRPO methods for flow models therefore replace the inference-time ODE with a stochastic differential equation (SDE) during training. Although the ODE and SDE share the same marginal distributions in continuous time, their finite-step discretizations can differ substantially. In particular, SDE rollouts often become blurry as the exploration noise increases, creating a mismatch between the samples used for reinforcement learning and those generated by the test-time ODE sampler. We introduce LC-GRPO, a flow-based GRPO framework with Langevin correction. Each rollout transition first takes an inference-aligned ODE Euler step and then applies a stochastic Langevin correction targeting the marginal distribution at the resulting timestep. The required score is recovered directly from the flow velocity, requiring no additional score model, while the resulting transition remains an isotropic Gaussian with a tractable likelihood for policy optimization. We theoretically show that, under suitable conditions, one Langevin correction step reduces the Wasserstein error of an imperfect ODE Euler step. At a matched randomness level, we further show that the proposed transition can be more accurate than the standard Euler--Maruyama discretization of the reverse SDE. Experiments on SD3.5-Medium, FLUX.1-Dev, and HunyuanVideo demonstrate that LC-GRPO consistently improves reward optimization across text-to-image and text-to-video tasks, preserves generation quality, and substantially narrows the gap between stochastic training rollouts and deterministic test-time ODE inference.

Yingqing Guo, Hui Yuan, Zijian He +2

RL for Video Generation RL for Image Generation Policy Gradient Methods Flow-Based Generative Modeling RL for Generative Models

Jul 31, 2026cs.LG

Convergence and Regret of the Policy Gradient for Multi-Armed Bandits in Diffusion Environment

This paper studies the policy gradient update for a multi-arm bandit problem in diffusion environment that is described by a stochastic differential equation (SDE) under the continuous-time reinforcement learning framework by Wang et al. (2020), Jia and Zhou (2022b). With the logit parameterization for the stochastic policy, we show that it converges almost surely to the optimal arm under an arbitrary constant learning rate. Furthermore, we derive the non-asymptotic regret upper bound when the constant learning rate is below a time-invariant threshold; and the regret bound has order

O(\log T)

. We improve the analysis in Lattimore (2026a) for the same SDE by constructing a novel Lyapunov function and demonstrate the transparency of analyzing policy gradient using the tools in SDEs. In addition, the same Lyapunov function is also helpful in analyzing the discrete-time policy gradient algorithm.

Yanwei Jia, Du Ouyang

Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong SAR · Department of Mathematical Sciences, Tsinghua University, Beijing, Beijing 100084, China

Multi-Armed Bandits Regret Minimization in RL Continuous-Time RL Policy Gradient Methods Policy Learning

Jul 28, 2026cs.AI

CoRT: Counterfactual Replay for Token-Level Rubric-Guided Policy Optimization

Rubric-based reinforcement learning enriches language model training by evaluating model outputs against explicit criteria. Yet in GRPO-style pipelines, these structured judgments are reduced to a scalar response-level reward and converted into a response-level advantage, which is broadcast uniformly to all generated tokens. This leaves no explicit mechanism for allocating credit within a response, even when different criteria are grounded in different spans, formatting decisions, or semantic choices. We propose CoRT, a token-level credit weighting method for rubric-conditioned GRPO. Instead of training an auxiliary token scoring model, CoRT uses counterfactual replay to rescore the same sampled response under the original rubric-conditioned prompt and a matched criteria-free prompt. The resulting tokenwise log-likelihood contrasts serve as a proxy for dependence on the rubric context. CoRT maps these contrasts to bounded, response-normalized weights and uses them to redistribute the signed GRPO advantage across tokens, without introducing an auxiliary scorer or changing the response-level reward. Experiments across instruction-tuned models and reward granularities show that CoRT improves over matched response-level GRPO in the vast majority of comparisons, with an average gain of 4.4 percentage points. The method remains competitive with learned token-level credit baselines while avoiding a separate relevance-learning stage. These results suggest that policy-internal counterfactual likelihood contrasts provide an effective training signal for within-response credit allocation while retaining the simplicity and stability of GRPO.

Bo-Wen Zhang, Junwei He, Wen Wang +5

State Key Laboratory of Novel Software Technology, Nanjing University · School of Intelligence Science and Technology, Nanjing University · ByteDance +1

Token-Level Credit Assignment Rubric-Based RL Policy Gradient Methods Credit Assignment Counterfactual Credit Assignment

Jul 25, 2026cs.LG

Finite-Time Analysis of the Natural Policy Gradient in Finite-Horizon Markov Decision Processes

Natural Policy Gradient (NPG) is a well-established Reinforcement Learning algorithm that underlies widely used methods such as Trust Region Policy Optimization and Proximal Policy Optimization, both of which have demonstrated strong empirical success. In this paper, we study exact NPG in finite-horizon Markov Decision Processes with known dynamics and horizon-dependent transition kernels. We provide the first finite-time convergence guarantees for this algorithm in this setting, for which we consider both constant and increasing step size regimes. With a constant step size

η_t=η

, we prove that NPG converges sublinearly with a rate of

\mathcal{O}(H^{2}/t)

after

t

iterations, where

H

is the horizon length. We also extend this constant step size analysis to linear MDPs in an exact population-projection oracle under a full support projection distribution, recovering the same sublinear rate as in the tabular setting. Furthermore, with increasing step sizes, we prove that this algorithm achieves a linear convergence rate of

\mathcal{O}\left(\left(1-\frac{1}{\vartheta_ρ}\right)^t\right)

for a problem-dependent constant

\vartheta_ρ> 1

, and the horizon-only robust schedule of the form

η_t=η_0(H/(H-1))^t

where

η_0>0

and

H \geq 2

, attains this same geometric rate.

Asha Barua, Sajad Khodadadian

Grado Department of Industrial and Systems Engineering, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061, USA.

Policy Gradient Markov Decision Processes Natural Gradient Methods Policy Gradient Methods Policy Learning

Jul 21, 2026cs.LG

Exposure-Based Reinforcement Learning to Rank

Reinforcement learning (RL) methods for learning-to-rank (LTR) can optimize (almost) any ranking goal, e.g., from precision or discounted cumulative gain to fairness-of-exposure or ranking distillation. However, standard RL is ineffective and computationally costly due to the enormous action space in LTR settings. Existing methods reach computational efficiency through custom gradient computation algorithms, but they are very complex to implement and often clash with auto-differentiation. Consequently, existing RL for LTR is not attractive to many practitioners. We reconsider RL for LTR while actively avoiding reliance on custom gradients. Contrary to the existing approaches, we focus on variance reduction and GPU computation. In doing so, we discover that high sample-efficiency can be reached through baseline corrections and partial marginalization. Furthermore, we propose an abstraction that places gradient estimation behind a document-exposure distribution, this enables seamless plug-and-play integration with auto-differentiation. Thereby, one only has to implement a loss as a differentiable function of exposure and RL for LTR can optimize it using auto-differentiation. Our experimental results reveal that our new exposure-based RL for LTR approach converges considerably faster and at significantly higher ranking performance than existing custom gradients, with no additional costs in computation time when using GPUs. In contrast, existing custom gradients result in severe stability issues when converging over many epochs, which never occur for our methods. Thus, we considerably improve RL for LTR methodology by increasing its effectiveness, efficiency, and ease of application.

Harrie Oosterhuis, Rolf Jagerman, Zhen Qin +1

University of Amsterdam · Google DeepMind

Reinforcement Learning Learning to Rank Policy Gradient Methods

Jul 20, 2026cs.MA

Scalable Policy Optimization for Networked Multi-Agent Reinforcement Learning with Continuous State-Action Spaces

Learning local policies for continuous networked systems requires accounting for the effects of decisions beyond each agent's observation neighborhood. Spatial decay limits these effects, but a finite critic must also control representation and estimation errors throughout policy optimization. We analyze the Continuous Distributed Coupled Policy Gradient (CDCPG) algorithm using local random Fourier features and least-squares temporal-difference critics. For features that retain the boundary inputs required by the local dynamics, we derive an action-value representation with separate spatial and finite-feature residuals. A global integrated transition-approximation bound and a projected Bellman argument control population prediction error without an inverse-conditioning multiplier. We then quantify the dependence of critic estimation on feature excitation and dimension, and construct simultaneous lower confidence bounds for temporal-difference conditioning along the executed iterates. Combining critic error with localized reward aggregation bounds the expected squared projected-gradient mapping by an optimization term and an explicit residual separating spatial approximation, finite features, and omitted distant rewards. For fixed neighborhoods and feature dimension, the shared-oracle sample count is inverse-squared in the excess squared-stationarity accuracy, up to logarithmic factors. The guarantee assumes known local dynamics and rewards, independent discounted-occupancy samples, and stated excitation, decay, and smoothness conditions, and is conditional on favorable feature draws. Numerical studies illustrate related implementations on a linear-coupled-quadratic benchmark.

Dongming Wang, Pengcheng Dai, Wenwu Yu +1

Department of Electrical and Computer Engineering, University of California, Riverside, CA 92521, USA · Engineering Systems and Design Pillar, Singapore University of Technology and Design, Singapore 487372 · Frontiers Science Center for Mobile Information Communication and Security, School of Mathematics, Southeast University, Nanjing 211102, China +1

Multi-Agent Control Temporal-Difference Learning Policy Gradient Methods Decentralized MARL Multi-Agent Reinforcement Learning Offline MARL

Jul 17, 2026cs.LG

CLaC@FinMMEval 2026 Task 3: Sentiment-Augmented Deep Reinforcement Learning for Active Trading -- An Alpha-Reward Approach

This paper presents our system for Task 3 of the CLEF 2026 FinMMEval Lab, which requires daily long, flat, or short trading decisions for Bitcoin (BTC) and Tesla (TSLA) using news and historical market data. We formulate the problem as a discrete-action Markov Decision Process and compare four deep reinforcement learning algorithms: Policy Gradient (PG), Proximal Policy Optimization (PPO), Deep Q-Learning (DQL), and Deep Deterministic Policy Gradient (DDPG). The agents use technical indicators, cyclical calendar encodings, and daily news sentiment scores produced by LLaMA 3.2 1B. To reduce overfitting and align training with the objective of outperforming buy-and-hold, we introduce an alpha reward based on excess market return and randomize episode start dates. Hyperparameters are optimized with Ray Tune over 180 trials per algorithm-asset pair, with early stopping and model selection based on validation Sharpe ratio. On the CLEF Task 3 test set, DDPG achieves the strongest overall performance. DQL was selected a priori for the live endpoint because it obtained the highest validation Sharpe ratio, with selection performed without access to the test period. For TSLA, DDPG and DQL achieve cumulative returns of 54.96% and 52.62%, respectively, compared with 16.45% for buy-and-hold. For BTC, DDPG achieves a positive return of 1.58% while buy-and-hold declines by -34.27%. The results also reveal a substantial validation-to-test generalization gap, highlighting the difficulty of transferring policies selected in bull-market conditions to a bear-market regime.

Andrei Neagu, Eeham Khan, Leila Kosseim

Department of Computer Science and Software Engineering, Concordia University, Montréal, Canada

Reinforcement Learning Deep Q-Learning Policy Gradient Methods Deep Deterministic Policy Gradient Reward Design for RL Finance+1

Jul 16, 2026cs.CL

Mask-Aware Policy Gradients for Diffusion Language Models

Reinforcement learning has proven effective for improving reasoning in large language models, but extending it to Masked Diffusion Language Models (MDLMs) remains challenging due to the intractability of the log-likelihood estimation. Existing approaches approximate this log-likelihood by modeling only the token predictions, ignoring the order in which positions are unmasked during generation. We observe that MDLM generation involves two decisions at each step: what tokens to place at each masked position and which positions to remask. We formalize this as a two-stage action MDP, showing that the policy gradient naturally decomposes into a token term and a masking term. Combining optimization of both terms leads to state-of-the-art outcomes on mathematical reasoning and coding benchmarks, with scores of 87.1% on GSM8K and 53.4% on MBPP.

Haran Raajesh, Kulin Shah, Adam Klivans +1

Department of Computer Science The University of Texas at Austin

Masked Diffusion Models RL for Language Model Reasoning Policy Gradient Methods RL for Diffusion Models

Jul 15, 2026cs.LG

Branching Policy Optimization: Sandbox-Native Language Agent Reinforcement Learning

Reinforcement learning has emerged as the dominant paradigm for training large language model (LLM) agents that interact with executable sandboxes. State-of-the-art algorithms such as PPO, RLOO, and GRPO inherit their rollout topology from RLHF: for each prompt, N independent trajectories are sampled from the initial state, and an advantage is computed by subtracting a group baseline. This design ignores a defining property of agent sandboxes. They are deterministic, snapshottable, and resumable from any intermediate state. We argue that this property enables a fundamentally different rollout topology: rather than N independent trees of depth T, one can construct a single tree of N leaves whose siblings share prefixes, and therefore share variance. We instantiate this idea as Branching Policy Optimization (BPO), a sandbox-native RL algorithm that (i) adaptively snapshots the sandbox at high-entropy decision points along a backbone trajectory, (ii) forks K alternative actions per branch point and rolls out each to termination, and (iii) computes per-step advantages from sibling returns rather than from independent prompts. We prove this estimator is unbiased and has strictly lower variance than the trajectory-level baseline, with the reduction equal to the prefix-explained portion of return variance. On WebShop, ALFWorld, and SWE-bench Verified with Qwen2.5-7B and Llama-3.1-8B backbones, BPO improves success by 3.6--6.1 absolute points over GRPO and RLOO at matched compute, halves gradient-norm variance, and matches the best baseline using 38% fewer policy updates.

Bowei He, Yankai Chen, Xiaokun Zhang +1

Mohamed bin Zayed University of Artificial Intelligence, Abu Dhabi, UAE · McGill Univeristy, Montreal, Canada · City University of Hong Kong, Hong Kong SAR.

Reinforcement Learning Policy Gradient Methods Policy Learning Sample-Efficient RL RL for LLM Agents

Jul 8, 2026cs.LG

UP: Unbounded Positive Asymmetric Optimization for Breaking the Exploration-Stability Dilemma

Reinforcement learning (RL) has become the standard paradigm for enhancing the complex reasoning capabilities of large language models (LLMs). To achieve sample efficiency, modern RL frameworks rely on importance sampling (IS). However, these algorithms suffer from an exploration-stability dilemma. Pure IS often leads to catastrophic training instability, while standard clipping mechanisms used to mitigate this instability strictly constrain the policy update budget. By formalizing the concept of Probability Capacity (Cap), we reveal that conservative clipping structurally stifles exploration by prematurely truncating the update budget for correct but low-confidence reasoning paths. To break free from these constraints, we propose Unbounded Positive Asymmetric Optimization (UP), a universal and plug-and-play objective. UP theoretically restructures the optimization process by anchoring the policy to its current state via the stop-gradient operator. This asymmetric design unleashes unclipped, stable gradients for positive advantages to maximize exploration, while maintaining standard clipping safeguards for negative advantages to prevent training instability. Furthermore, our formulation readily extends across different optimization granularities, including token-level (GRPO, DAPO) and sequence-level (GSPO) frameworks. Extensive experiments demonstrate that UP enhances exploration capacity and achieves superior reasoning accuracy across diverse RL algorithms (DAPO, GSPO, and GRPO), model architectures (Dense, MoE, and vision-language), and training modalities (language and multimodal), validating UP as a truly universal plug-and-play enhancement for RL-based training.

Chongyu Fan, Pengfei Liu, Jingjia Huang +2

ByteDance Seed · Michigan State University

RL for Language Model Reasoning Policy Optimization RL Exploration Policy Gradient Methods RL Post-Training

Jul 3, 2026cs.LG

ACPO: Adaptive Credit Policy Optimization via Fine-Grained Surrogate Entropy

Reinforcement Learning (RL) has substantially improved the reasoning ability of large language models (LLMs), but sparse outcome rewards still make token-level credit assignment difficult. Existing scalable RL methods typically assign trajectory-level rewards uniformly across tokens, while recent entropy-aware approaches either rely on coarse detached heuristics or directly optimize true entropy, which can introduce non-local gradient components misaligned with sampled-token policy updates. We propose Adaptive Credit Policy Optimization (ACPO), a token-level credit assignment framework based on a mode-local surrogate entropy. ACPO asymmetrically modulates policy updates by emphasizing uncertain decisions in successful rollouts and overconfident tokens in failed rollouts. We show that the surrogate admits deterministic entropy bounds and, under modal alignment and proximal updates, preserves the policy-gradient direction to leading order. Experiments on mathematical reasoning and coding benchmarks, including AIME 2025 and HumanEvalPro, show that ACPO consistently improves over strong RL baselines such as DAPO, GTPO, and SAPO.

Zijun Xie, Yuyang You, Yongzhi Li +6

Peking University · Baidu Inc. · Kuaishou Inc.

Token-Level Credit Assignment RL for Language Model Reasoning Step-Level Credit Assignment in RL Maximum Entropy RL Policy Gradient Methods Sparse-Reward RL+1

Jul 2, 2026cs.LG

One More Time: Revisiting Neural Quantum States from a Reinforcement Learning Perspective

Neural quantum states (NQS) provide a flexible and scalable framework for approximating quantum many-body wavefunctions. Among NQS parameterizations, autoregressive models are especially attractive because they enable exact, independent sampling from the Born distribution, avoiding the autocorrelation and mixing issues of Markov chain methods. Yet their optimization remains comparatively underexplored: Adam is a scalable method but ignores function space geometry, while stochastic reconfiguration is principled but costly and numerically fragile in large models. To address this gap, we show that variational energy minimization can be viewed as an advantage policy-gradient problem over the Born distribution, motivating trust-region optimization for NQS training. We introduce Proximal Wavefunction Optimization (PWO), a principled trust-region algorithm that clips probability-ratio changes in the amplitude channel and phase increments in the phase channel. PWO avoids explicit matrix inversion, reuses samples across multiple updates, and combines the scalability of first-order optimization with theoretical guarantees. Across Ising and frustrated

J_1

-

J_2

one- and two-dimensional spin systems, PWO improves stability and wall-clock convergence over Adam, minSR, and SPRING. Finally, we fine-tune a

1.5

B-parameter RWKV-7 model, demonstrating NQS optimization at a scale over three orders of magnitude beyond prior work.

Juan Agustín Duque, Sergio García Heredia, Vinicius Hernandes +4

Mila Quebec AI Institute, Université de Montréal, Montréal, Canada · Applied Quantum Algorithms ⟨aQaL⟩, LIACS & LION, Leiden University, Leiden, Netherlands · QuTech and Kavli Institute of Nanoscience, Delft University of Technology, Delft, Netherlands +1

Neural Quantum States Second-Order Optimization Policy Gradient Methods Trust-Region Optimization Quantum Many-Body Physics

Jul 1, 2026math.OC

Mean Field Reinforcement Learning

This monograph provides an introduction to mean field reinforcement learning through the lens of Markov decision processes arising from large-population stochastic control with mean field interactions and common noise. Starting from the connection between multi-agent reinforcement learning and mean field control, it develops the probabilistic, mathematical, and control-theoretic framework needed to formulate representative-agent learning problems, analyze their relationship with finite-population systems, and study both general and linear-quadratic models. The presentation includes dynamic programming principles, propagation-of-chaos limits, and theoretical analyses of tabular Q-learning and policy-gradient methods. It also discusses numerical implementations, including tabular schemes and deep reinforcement learning methods such as deep deterministic policy gradient. The goal is to give readers a coherent bridge between mean field control theory and reinforcement learning methodology, emphasizing the mathematical structure of the problems and the design of tractable learning approaches for large stochastic populations.

René Carmona, Mathieu Laurière

Department of Operations Research and Financial Engineering & Program in Applied and Computational Mathematics, Princeton NJ 08544, USA · Shanghai Frontiers Science Center of Artificial Intelligence and Deep Learning; NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai; NYU Shanghai, 567 West Yangsi Road, Shanghai, 200126, People’s Republic of China

Reinforcement Learning Q-Learning Policy Gradient Methods Policy Learning

Jun 30, 2026cs.LG

GRPO, Dr. GRPO, and DAPO Are Three Operations on One Number: The Group-Standard-Deviation Identity

Three of the most popular methods for training language models to reason look like three different tricks. They are not. All three adjust a single number: standard deviation, reflecting how much a prompt's sampled answers disagree. When such a model is trained, it answers each problem many times, and an automatic checker marks every answer right or wrong. The standard deviation of those marks measures the disagreement: largest when the answers split evenly between right and wrong, and zero when they all agree. Group Relative Policy Optimization (GRPO) divides by this number, GRPO Done Right (Dr. GRPO) drops the division, and Decoupled Clip and Dynamic Sampling Policy Optimization (DAPO) discards the groups where it is zero. Each is presented as its own fix, yet this paper proves they are three settings of one dial. That dial is not cosmetic: for right-or-wrong rewards, the disagreement is exactly the size of the training update, the group-standard-deviation identity. A split group teaches the most, while a unanimous group teaches nothing and falls silent. The same result says which problems deserve the most weight and how many tries each one needs. This paper confirms the intuition on a large real difficulty dataset (Big-Math) and in a controlled training run. What looks like a harmless normalization step is the dial that decides where learning happens and how strongly.

Yong Yi Bay, Kathleen A. Yearick

PhD, University of Illinois at Urbana-Champaign

Reinforcement Learning RL for Language Model Reasoning Group Relative Policy Optimization Policy Gradient Methods

Jun 30, 2026cs.AI

Smart charging of large fleets of Electric Vehicles: Independent Multi-Agent Reinforcement Learning approaches

The electrification of transportation through electric vehicles introduces new challenges for power grid management, such as increased peak demand, voltage fluctuations, line overloads, and the integration of variable renewable energy sources. To enable efficient integration of EVs while minimizing costs for users and avoiding network overloads, implicit coordination between EVs is required. This work compares two independent multi-agent reinforcement learning approaches for optimizing such decentralized EV charging: contextual combinatorial bandits and policy gradient algorithms. Using a realistic simulation environment with autonomous agents making decisions based on local environmental information (including price signals, state-of-charge, and temporal constraints), we evaluate their performance across varying congestion levels, and mixed-strategy configurations with heterogeneous agent groups under dynamic electricity pricing derived from real photovoltaic production data.

Xavier Rate, Eloann Le Guern, Raphaël Féraud +8

Orange · ENS Rennes · IMT Atlantique +1

Multi-Agent Coordination Electric Vehicle Charging Policy Gradient Methods Contextual Bandits Decentralized MARL Power Systems