KL-Regularized RL

RL: Reinforcement Learning

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3 papers in the last four weeks, with none the four weeks before. 0.0% of all new papers.

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Latest papers 36

Oct 6, 2026cs.LG

On KL-Regularized Policy Optimization

Asynchronous reinforcement learning (RL) for large language model (LLM) agents trains one policy on trajectories generated by another: rollouts come from stale checkpoints, and the inference engine's probabilities differ from the trainer's even at identical parameters. Standard remedies either clip importance ratios, which biases the update, or, as in GRPO, sample a group of responses per prompt, which is costly when episodes are long. We propose KL-Regularized Policy Optimization (KLPO), a framework that anchors the KL regularizer at the sampler. The regularized improvement step then has a closed-form Gibbs solution, and KLPO fits its log-ratio optimality condition by least squares on the sampler's own trajectories, so the sampler probability enters through a log-ratio and no importance weights are needed. Profiling out the regression intercept replaces the intractable log-partition function with the signal's sampler mean plus a sampler-to-trainer KL divergence. For token-level policy mirror descent targets, we show that the resulting gradient can be computed from terminal returns without a critic, via sampler-centered scores or a single trajectory residual, even under stochastic tool outputs. We further prove that independent Monte Carlo estimates of the KL term keep these gradients unbiased, derive the exact KL gap of cheaper top-

K

and binary approximations, and show that SPPO, GPO, REBEL, and BPO arise as special cases of KLPO. The result is a critic-free update that uses one rollout per prompt and requires neither a learned normalizer nor a group of responses.

Yifan Zhang

Princeton University

RL for LLM Agents KL-Regularized RL Off-Policy RL Asynchronous RL Critic-Free RL

Oct 1, 2026cs.LG

FERPO: Forward Entropy-Regularized Policy Optimization

Several state-of-the-art methods for online reinforcement learning in continuous control improve policies using action gradients of a learned critic. However, critics are typically trained to predict returns, and accurate value predictions do not necessarily yield accurate action derivatives, potentially leading to unreliable policy updates. We propose Forward Entropy-Regularized Policy Optimization (FERPO), an on-policy maximum entropy reinforcement learning algorithm that performs policy improvement using critic values without differentiating the critic with respect to actions. FERPO derives an optimal target action distribution from a policy-improvement objective regularized by entropy and Kullback-Leibler (KL) divergence. We then fit the actor to this target by minimizing a forward-KL objective, estimated using self-normalized importance sampling (SNIS) with actions drawn from the rollout policy. By limiting the target distribution's deviation from the rollout policy, the KL regularization helps keep these importance weights well behaved. In contrast to reverse-KL objectives, which can favor a subset of the target distribution's modes, the forward-KL objective encourages coverage of multiple high-value modes and thereby promotes exploration. Experiments and ablations on MuJoCo Playground and ManiSkill show competitive performance and sample-efficiency gains. Computational benchmarks also demonstrate faster actor updates than Relative Entropy Pathwise Policy Optimization (REPPO).

Sebastian Sanokowski, Alireza Sarmadi, Majid Khadiv

Applied and Theoretical Aspects of Robot Intelligence (ATARI) Lab, Munich Institute of Robotics and Machine Intelligence (MIRMI), Technical University of Munich

KL-Regularized RL Policy Optimization Maximum Entropy RL Continuous Control Policy Learning

Sep 17, 2026cs.AI

Steering Equilibrium Selection in Regularized Self-Play via the Reference Policy

Regularized self-play -- the family behind DeepNash's Stratego play -- drives a two-player zero-sum policy to a Nash equilibrium by best-responding to a slowly moving, entropy-regularized reference policy

ρ

. When the game has a polytope of value-equivalent equilibria, the regularizer silently breaks the tie: with a uniform reference it selects the maximum-entropy member, the I-projection of

ρ

onto the Nash set. Can the reference be used to choose the equilibrium on purpose? On five exactly solvable games plus a 2-D polytope, with exact best responses and equivalence tests over independent seeds, anchoring the reference at a target member and refining steers self-play to that member with mean coordinate error 0.007 at median exploitability

5\times10^{-5}

, TOST-equivalent to the request within

\pm0.05

; the anchoring persists through refinement and follows the reference, not the initialization. Selection follows the reach-weighted I-projection (slope 0.969 [0.950, 0.987]). We report with equal emphasis where the story breaks: fixed off-manifold references cost 0.08-0.25 exploitability; stiff or flat families require a smaller mirror step, set by a pre-registered rule; boundary targets undershoot; curvature predicts where boundary saturation bites (rank correlation 0.90, p=0.037) while interior precision is curvature-independent. Table and MLP steering maps are equivalent within

\pm0.03

at every target (30 seeds); matched control arms show attention's robust signature is excess seed variance, any systematic shift bounded at 0.018 and not significant. Against a best response the selection-robustness trade-off is degenerate: steering matters only against fixed, non-equilibrium opponents. The recipe -- anchor the reference at the desired member and refine -- reinterprets the KL anchor of RLHF-style RL as a selection knob, not only a stability leash.

Luis Leal

Nash Equilibrium Self-Play RL KL-Regularized RL Zero-Sum Games

Sep 14, 2026cs.LG

A Unified and Constrained View of Regularization-Based Robust Reinforcement Learning

Regularization-based methods have become a standard approach for training Deep Reinforcement Learning policies against adversarial input perturbations. In this paper, we unify these methods by deriving new upper bounds on the performance gap between the nominal and worst-case policies. Each upper bound is expressed as an existing regularization objective plus a KL-divergence penalty between the nominal and worst-case policies, which further explains why adding a KL penalty improves robustness in practice. Building on these bounds, we formulate robust training as a constrained optimization problem, showing that existing methods correspond to the special case of a fixed Lagrange multiplier. We instead update the multiplier jointly with the policy to automatically tune the regularization weight. Finally, we conduct extensive adversarial evaluations across several continuous control tasks to validate our theoretical analysis.

Amine Andam, Jamal Bentahar, Mustapha Hedabou

Mohammed VI Polytechnic University · Khalifa University · Concordia University

KL-Regularized RL Adversarial Robustness Constrained RL Robust RL Policy Learning

Aug 3, 2026cs.LG

Toward Plasticity-Preserving KL Regularization for Capability Retention in LLM Reinforcement Learning

Reinforcement learning (RL) has become a central paradigm for large language model (LLM) post-training, but optimization toward new objectives can degrade capabilities already present in the base model. KL regularization is widely used to mitigate such forgetting by constraining policy drift toward a reference model. However, standard full-policy KL regularization constrains the entire response distribution and may unnecessarily restrict exploration and target-task learning. This raises a natural question: can a more precise constraint preserve existing capabilities while minimizing interference with learning new tasks? To this end, we propose \underline{Co}rrectness-Conditioned \underline{KL} Regularization (CoKL), a conditional regularization framework that narrows the preservation constraint from the full output distribution to correctness-conditioned response distributions. We instantiate CoKL with forward KL divergence and derive a practical finite-group training objective for RL-based LLM post-training. At the population level, CoKL decouples the total probability assigned to correct responses from their correctness-conditioned distribution, thereby regularizing the relative probability allocation among reference-supported correct responses without directly anchoring incorrect outputs or total correctness mass. We further show that full-policy forward and reverse KL regularization induce a strict optimal correctness gap when the reference policy is imperfect, whereas CoKL avoids this limitation. Experiments in controlled multi-solution environments and continual post-training settings across multiple model scales demonstrate that CoKL achieves a more favorable balance between target-task improvement and prior-capability retention than existing regularization methods. Our code is available at https://github.com/Lumina04/CoKL.

Li Wang, Xiaodong Lu, Xiaohan Wang +4

1Meituan · 2Nanyang Technological University

Continual Learning for LLMs KL-Regularized RL RL Post-Training

Aug 3, 2026cs.RO

A Forward-Inverse Dynamic Game Framework for Enhanced Multi-Agent Trajectory Planning

This paper studies feedback Nash equilibrium (FBNE) seeking for multi-agent trajectory planning in nonlinear dynamical systems with unknown agents' objectives and state-dependent inter-agent coupling. While dynamic game theory provides a principled framework for such problems, existing approaches typically assume fully rational agents with known objectives or rely on fixed regularization, limiting their ability to capture bounded rationality and spatially varying interaction intensity in safety-critical settings. To this end, we propose a KL-regularized dynamic game with a state-dependent weight that adaptively balances optimality and behavioral priors. To infer unknown cost parameters from demonstrated behaviors, we develop a context-aware inverse game module based on maximum-entropy inverse reinforcement learning with physics-informed regularization, ensuring structural consistency with the forward game. We establish per-iteration well-posedness of the regularized local game and show that the adaptive weighting function remains Lipschitz continuous under bounded nominal-trajectory updates. Numerical simulations and multi-robot experiments on cooperative navigation and merging scenarios validate the effectiveness of the proposed framework.

Tianle Liu, Youcheng Niu, Jing Zeng +2

College of Control Science and Engineering, Zhejiang University, Hangzhou 310027, China

KL-Regularized RL Game Theory Multi-Robot Coordination Multi-Agent Planning

Jul 31, 2026cs.LG

Abstention as an Action Can Kill Both the Reward Gradient and the KL Anchor: Collapse Law and Repair for Error-Penalized Reinforcement Learning

Error-penalized scoring rules (

+1

for a correct answer,

-λ

for a wrong one,

0

for abstaining) are increasingly prescribed against hallucination: a rational agent facing such a rule answers exactly when its correctness probability exceeds Chow's threshold

t^\ast=λ/(1+λ)

. We prove that a KL-anchored gradient learner can do the opposite. When abstention is a discrete action, the reward gradient and the anchor's restoring force are throttled by the same gate-saturation factor and die together: under explicit conditions (among them, blanket answering loses score in expectation and prompts share a bounded readout) the model drifts toward refusing everything, its mean training reward rising to zero like

1/t

in training time

t

, so the curve reads as improvement while coverage collapses. The advantage estimator compounds the failure: in its sparse-answer regime, group normalization silently replaces every designed penalty with an effective penalty of one, moving the learned threshold from

t^\ast

to

1/2

. The repair is structural: train a mandatory confidence report with a strictly proper score plus a correctness reward, and abstain only at deployment by thresholding the report. The always-emitted report has no gate to saturate, so no shared factor can kill its reward gradient and its anchor together, and its calibrated optimum is attracting. Simulations confirm every prediction, and experiments on language models at two scales confirm the mechanism live: the rule silences questions the models demonstrably still solve within ten optimizer steps, an ablation isolates the cause, and report-level training raises coverage, accuracy, and calibration together.

Xujun Che, Yuchen Yuan, Weida Zhao +1

Department of Cybersecurity, University of North Carolina at Charlotte, Charlotte, NC, USA · Department of Information Sciences and Technology, George Mason University, Fairfax, VA, USA · Department of Computer Science and Software Engineering, Auburn University, Auburn, AL, USA +1

Reinforcement Learning KL-Regularized RL Language Model Calibration RL Post-Training LLM Abstention

Jul 30, 2026cs.LG

$β$ -OPSD: Deriving with Policy Optimization, Training with Self-Distillation

On-policy self-distillation (OPSD) is a promising approach to improve reasoning language models, but it remains brittle in practice: making it work reliably often requires substantial engineering effort. We identify a structural source of this difficulty: vanilla OPSD is precisely the

β=1

member of a broader policy-optimization family, where

β

weights the KL penalty anchoring the student to a reference policy. This equivalence turns

β

from an implicit value fixed at one into a controllable regularization parameter, yielding a more general formulation that trades off proximity to a reference policy against privileged teacher guidance. We introduce

β

-OPSD and derive its optimal policy as a geometric interpolation between the reference policy and the privileged teacher. Directly optimizing this objective with reinforcement learning, however, would be costly and high-variance. Rather than optimize the RL objective directly, we turn its closed-form solution into a distillation target. Each value of

β

selects a target along the reference-to-teacher path, which we implement efficiently by mixing their token-level logits. In this way, inexpensive distillation approximates the solution of expensive policy optimization. Return-to-go credit assignment further aligns token updates with the sequence-level objective while retaining the simplicity of OPSD. Experiments on mathematical reasoning benchmarks show that

β

-OPSD consistently outperforms vanilla OPSD, improving optimization stability and downstream reasoning performance. Our results provide a principled route from self-distillation to policy optimization and back without sacrificing the efficiency that makes OPSD practical.

Jiawei Xu, Minghui Liu, Juzheng Zhang +2

University of Maryland, College Park

KL-Regularized RL On-Policy Self-Distillation RL for Language Model Reasoning Language Model Distillation Policy Learning

Jul 29, 2026cs.LG

Post-Training at the Edge of Detectability: A Game-Theoretic Approach to Fine-Tuning

Reinforcement learning (RL) fine-tuning is widely used in language model training to improve performance on a target task while limiting drift from a reference policy. A standard way to balance this trade-off is via a KL-regularized RL objective, although this formulation does not by itself provide a principled way to set the regularization coefficient. In practice, the coefficient is typically chosen heuristically or via hyperparameter search, which can lead to unnecessary overhead in training cost or undesirable reward-retention trade-offs. We instead propose a game-theoretic framework that gives this trade-off an explicit statistical interpretation. Specifically, we study a sequential game in which an agent chooses a policy to maximize cumulative reward while a monitor observes policy outputs over time and tests for deviations from the reference policy. Although not originating from the same perspective, we show that the resulting equilibrium policy can nonetheless be expressed as the solution to a KL-regularized RL problem for an optimal regularization parameter that can be viewed as maximizing reward per unit of statistical distinguishability. Drawing on classical results from concave-convex fractional programming, we provide a principled method for learning this equilibrium coefficient via reduction to the KL-regularized RL objective, thus allowing for flexible integration into standard fine-tuning pipelines. In experiments with Qwen3-8B and Llama-3.2-1B, we show that our methods result in competitive reward-retention trade-offs in a continual learning setting, and illustrate how our framework may be used to audit API providers serving open-source models.

Keegan Harris, Brian W. Lee, Ian Waudby-Smith +3

University of California, Berkeley · Inria & École Normale Supérieure

Reinforcement Learning KL-Regularized RL RL Fine-Tuning

Jul 11, 2026cs.LG

ARMOR: Stabilizing On-Policy LLM RL with Off-Policy Anchor Samples

Reinforcement learning (RL) has significantly enhanced the reasoning capabilities of large language models (LLMs), yet the training process remains notoriously fragile. In this work, we investigate a critical source of this instability: over-optimization, where models exploit training heuristics at the expense of generalizable reasoning. While reverse KL regularization is the standard defense against such degradation, our analysis reveals that it is often insufficient in this regime, as it fails to ensure comprehensive coverage of the reference distribution. To address this, we propose ARMOR (Anchor Rollout and Mixed Optimization for RL), a framework that shifts the paradigm from passive penalty to active sample stabilization. ARMOR comprises two key components: (1) Anchor Rollout, which leverages off-policy data from the reference policy to preserve established solution patterns; and (2) Mixed Optimization, which reformulates the policy objective to enable controlled exploration without relying on auxiliary losses. Extensive experiments on reasoning benchmarks validate that ARMOR effectively mitigates validation collapse, enabling sustained performance improvements over extended training horizons.

Kexin Huang, Junkang Wu, Jinda Lu +7

University of Science and Technology of China · Peking University · Dartmouth College

Reinforcement Learning KL-Regularized RL RL for Language Model Reasoning RL Post-Training

Jul 11, 2026cs.CV

REVA-PO: Stabilizing Reinforcement Learning for Chest X-ray Report Generation

Automated chest X-ray report generation has recently benefited from reinforcement learning (RL) and large language models. However, RL training often suffers from instability or limited exploration due to fixed Kullback-Leibler (KL) regularization and a static reference policy that accumulates KL pressure over time. We propose Response-Weighted and Validation-Anchored Policy Optimization (REVA-PO), a RL framework that stabilizes long-term training via Response-Weighted Regularization (RER) and Validation-Anchored Policy Reset (VAPR). RER dynamically adjusts per-response KL weights based on advantage and reference-policy entropy, relaxing constraints for high-quality responses while tightening them for low-quality ones. Complementarily, VAPR periodically synchronizes the reference and current policies to the best validation checkpoint, resetting accumulated regularization pressure to expand the viable exploration space. To ensure a robust starting point, we employ a three-stage pipeline consisting of warm-up training, classifier-guided supervised fine-tuning, and RL. Extensive evaluations on MIMIC-CXR and IU-Xray demonstrate that REVA-PO sets new state-of-the-art benchmarks in both linguistic quality and clinical accuracy. Notably, BLEU-4 improves by 5.1% on MIMIC-CXR and 3.6% on IU-Xray, while CheXpert F1 and RadGraph F1 scores increase by 4.5% and 12.8%, respectively, over prior leading methods. The code is publicly available at https://github.com/LiGuo12/REVA_PO/.

Li Guo, Anas M. Tahir, Z. Jane Wang

University of British Columbia, Vancouver, BC, Canada

Radiology Report Generation Radiology VLMs KL-Regularized RL RL Post-Training RL for VLMs

Jun 30, 2026cs.LG

On the Convergence of Self-Improving Online LLM Alignment

The Self-Improving Alignment (SAIL) algorithm addresses distribution shift by reducing a bilevel formulation of the problem to an efficient, single-level method. Empirically, SAIL has demonstrated strong performance on this task. However, a formal analysis of its convergence properties has been lacking. We identify a key theoretical challenge: the standard SAIL objective function is not guaranteed to be strongly concave due to unfavorable properties of its Hessian. To address this limitation, we propose a regularized objective, SAIL-RevKL, which incorporates a reverse Kullback-Leibler (KL) divergence penalty to improve the optimization landscape. Our central theoretical contribution is to prove that this regularized objective satisfies the Polyak-Lojasiewicz (PL) condition within a bounded parameter space. We establish global convergence guarantees, achieving a near-linear sample complexity. We further validate the effectiveness and stability of SAIL-RevKL through empirical evaluations, demonstrating that it outperforms the vanilla SAIL on both MuJoCo benchmarks and LLM alignment tasks.

Xudong Wu, Pangpang Liu, Vaneet Aggarwal +1

The University of Hong Kong, Hong Kong SAR · Yale University, New Haven, CT, USA · Purdue University, West Lafayette, IN, USA

LLM Alignment Optimization Convergence Analysis KL-Regularized RL Language Model Self-Improvement

Jun 28, 2026cs.LG

CRAFT: Counterfactual Credit Assignment from Free Sibling Rollouts for Self-Distilled Agentic Reinforcement Learning

Self-distilled agentic reinforcement learning augments trajectory-level reward with a token-level distillation loss, using as its teacher the same policy conditioned on privileged context. The prevailing recipe gates this loss by a single scalar, the teacher-student log-probability gap. This signal is doubly limited: it is retrospective, scoring only the realised rollout and never the counterfactual ones, and it is sign-blind, never signalling when a teacher-preferred action would have harmed the trajectory. We introduce CRAFT, a three-pillar credit-assignment scheme that addresses both limitations. Pillar 1, Counterfactual Token Importance, reuses the G-1 sibling rollouts that GRPO already samples and importance-weights them by the log-probability gap to form a self-normalised estimate of the group-level counterfactual change in advantage from up-weighting teacher-preferred actions at each step; this yields a signed per-token credit at near-zero extra compute. Pillar 2 is an asymmetric controller that raises the distillation weight as it lowers the reference-KL weight along an exponential moving average of gate activity, and conversely. Pillar 3 polarises the KL penalty token by token, switching between a mode-seeking and a mode-covering update according to the sign of the credit. Each pillar has an independent switch that, when disabled, renders the loss and gradient byte-identical to the baseline in IEEE-754 arithmetic, so any measured gain is attributable to algorithmic change rather than implementation drift. We prove the estimator's consistency and a variance bound, give structural and bit-exact reproducibility guarantees, and evaluate CRAFT across three agentic environments, four model scales, and five end-to-end methods, plus two tabulated prior-work baselines. Among these is Adaptive-CRINGE, a comparator sharing Pillar 2 with CRAFT, isolating the counterfactual contribution.

Zibin Meng, Kani Chen

The Hong Kong University of Science and Technology

Agentic RL KL-Regularized RL Credit Assignment in RL Step-Level Credit Assignment in RL On-Policy Distillation Counterfactual Credit Assignment

Jun 26, 2026cs.LG

Regularized Reward-Punishment Reinforcement Learning

We propose KL-Coupled Policy Regularization (KCPR), a policy coordination framework for Reward-Punishment Reinforcement Learning (RPRL). Based on KCPR, we derive KL-Coupled Soft Optimality (KCSO) and develop its deep realization, klDMP. Unlike existing RPRL approaches that optimize reward-seeking and punishment-related policies largely independently, KCPR enables direct interactions between companion policies by treating each as a dynamically learned prior for the other. KCSO yields coupled soft-optimal policies and KL-regularized Bellman operators, allowing reward and punishment information to jointly influence value propagation. To improve learning stability, we introduce a companion-prior softening mechanism and evaluate separate replay-buffer designs for balancing reward- and punishment-related experience. Experiments in grid-world and Gazebo robotic navigation tasks demonstrate that klDMP improves safety and learning stability while maintaining competitive task performance compared with DQN, SQL and softDMP. These results suggest that policy-level coordination provides an effective mechanism for integrating multiple behavioral objectives and may serve as a useful design principle for reinforcement learning systems with interacting motivational processes.

Jiexin Wang, Eiji Uchibe

Dept. of Brain Robot Interface, ATR Computational Neuroscience Laboratories, 2-2-2, Hikaridai, Seikacho, Soraku-gun, Kyoto, 619-0288, Japan

Reinforcement Learning KL-Regularized RL Robotic RL Safe RL Policy Learning

Jun 22, 2026cs.LG

KLip-PPO: A per-sample KL perspective on PPO-Clip

Proximal Policy Optimization (PPO) is the standard policy-gradient algorithm for on-policy reinforcement learning. The literature presents it in two forms, a clipped surrogate that bounds the importance ratio between successive policies and a Kullback-Leibler penalty between them. These forms are treated as separate algorithms with their own gradients, their own hyperparameters, and their own reference implementations, and a sizeable body of empirical work compares them. We show that the gradient of the clipped surrogate is reproduced exactly by a Kullback-Leibler surrogate whose coefficient varies per sample, with closed-form dependence on the importance ratio and the advantage. The identity holds at every minibatch step and across the entire inner loop, and on five MuJoCo continuous-control benchmarks the two losses produce indistinguishable training curves. The reformulation exposes a structural feature of the clipped surrogate that the min notation hides. PPO-Clip's implicit per-sample penalty is a step function at the boundary of the trust region, and the shape of this coefficient is the natural design axis for generalising the algorithm. We sketch the resulting follow-up directions in the discussion.

Riccardo Colletti, Robin Holzinger

University of California, Berkeley

KL-Regularized RL Policy Gradient Methods Proximal Policy Optimization Policy Learning

Jun 8, 2026cs.LG

A Unifying Lens on Reward Uncertainty in RLHF

Reinforcement learning from human feedback (RLHF) is bottlenecked by reward hacking, where the policy exploits errors in a proxy reward model (RM) and produces high RM scores without genuine quality gains. A natural mitigation is pessimism: lowering rewards in regions where the RM is uncertain. However, standard scalar RMs provide no principled notion of uncertainty. We argue that the right object is a distributional reward model

p(r\mid x,y)

. Under either a Bayesian inference or a KL-distributionally robust optimization (KL-DRO) lens, the KL-regularized RLHF objective admits a closed-form effective reward

\tilde r(x,y) = \pmβ\log\mathbb{E}_p[e^{\pm r/β}]

. The pessimistic branch unifies the prior heuristics for RM ensemble aggregation: mean aggregation, worst-case optimization (WCO), and uncertainty-weighted optimization (UWO) all emerge as limits or truncations of this single expression. This also clarifies the implicit assumptions of each existing rule.

Ely Hahami, Yoel Zimmermann, Ray Zhou +1

Harvard College, Harvard University, Cambridge, MA, USA · John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, USA

Reward Modeling KL-Regularized RL Distributionally Robust RL RL from Human Feedback

Jun 4, 2026cs.LG

Online KL-Regularized Reinforcement Learning with Function Approximation under Misspecification

We study KL-regularized contextual bandits and episodic reinforcement learning (RL) under general function approximation with model misspecification. Existing guarantees rely on realizability and therefore do not extend to misspecified models, where classical regret bounds may fail. This work introduces KL misspecification formulations for contextual bandits and episodic RL and analyzes regression-based algorithms with Gibbs policy updates. High-probability KL-regret guarantees with explicit misspecification terms are established, recovering the standard realizable KL-regularized setting as a special case.

Haoyang Hong, Zichen Wang, Quanquan Gu +1

School of Electrical Engineering and Computer Science, Oregon State University · Department of Electrical and Computer Engineering and Coordinated Science Laboratory, University of Illinois Urbana-Champaign · Department of Computer Science, University of California, Los Angeles

Regret Minimization in RL Reinforcement Learning KL-Regularized RL Model Misspecification Contextual Bandits

May 26, 2026cs.LG

Trust Region Q Adjoint Matching

Off-policy reinforcement learning of pretrained flow policies remains challenging due to the instability of optimization arising from the multi-step sampling process. Recently, Q-learning with Adjoint Matching (QAM) addressed this by recasting policy improvement as a stochastic optimal control (SOC) problem guided by a learned critic. However, QAM inherits a fundamental fragility of critic-guided improvement, since small critic errors can be exponentially amplified and often lead to performance collapse. This paper introduces Trust Region Q Adjoint Matching (TRQAM), a stable off-policy fine-tuning algorithm that adaptively controls the path-space KL between the fine-tuned and pretrained policies through projected dual descent. Specifically, we adapt a trust-region parameter

λ

inside the sampling process of the flow policy and prove that

λ

exactly weights the path-space KL in the SOC objective. As a result, our method can tightly control the deviation from the pretrained policy within a prescribed KL budget, achieving stable off-policy RL. Through experiments on 50 OGBench tasks, TRQAM consistently outperforms prior methods in both offline RL and offline-to-online RL. In particular, TRQAM achieves an overall success rate of 68% in offline RL, substantially improving over the strongest baseline at 46%.

Yonghoon Dong, Kyungmin Lee, Changyeon Kim +2

KAIST AI · Seoul National University · RLWRLD

Reinforcement Learning KL-Regularized RL Offline RL Trust Region Policy Optimization RL Fine-Tuning Offline-To-Online RL

May 25, 2026cs.LG

Extreme Region Policy Distillation

Reinforcement learning for large language models faces a fundamental trade-off between sample efficiency and asymptotic performance: strictly on-policy methods discard trajectories after a single update, while off-policy reuse introduces distribution mismatch that existing trust-region techniques mitigate primarily by enforcing conservative optimization, often leaving rich training signals underutilized. To investigate this, we perform extensive off-policy updates on fixed data. Our experiments reveal that aggressive multi-step optimization brings rapid initial gains, but excessive updates cause trajectory probabilities to deviate and entropy to collapse, with performance plateauing early. Tightening KL constraints merely lowers the ceiling without resolving the degradation. This motivates Extreme Region Policy Distillation (ERPD), a two-stage framework that decouples sample efficiency from KL efficiency. The first stage performs weakly constrained off-policy optimization on fixed data to maximally extract training signals. The resulting policy provides token-level supervision. In the second stage, we distill these signals into the base policy under trust-region constraints, filtering harmful drift while preserving useful signals. The distilled policy achieves comparable or better performance with substantially smaller KL divergence, indicating that much of the first-stage divergence was spent on unnecessary drift rather than genuine improvement. Crucially, ERPD accommodates both strong and weak teachers: when aggressive optimization yields no stronger policy, even degenerate teachers provide effective supervision via alternative signal construction strategies. We validate ERPD on mathematical reasoning, showing gains for strong base models where on-policy training plateaus, and reliable improvements with weak teachers.

Changyu Chen, Xiting Wang, Rui Yan

Gaoling School of Artificial Intelligence, Renmin University of China · Wuhan University

KL-Regularized RL RL for Language Model Reasoning Language Model Distillation Knowledge Distillation Off-Policy RL

May 23, 2026stat.ML

How Neural Reward Models Learn Features for Policy Optimization: A Single-Index Analysis

Reward modeling is not only a prediction problem: in KL-regularized policy optimization, the learned reward is exponentiated to define the deployed policy, so downstream value depends on errors in reward-tilted regions. We study this feedback in a Gaussian single-index model with

r^*(x) = σ^*(\langle θ^*, x\rangle)

and

x \sim N(0, I_d)

. We analyze a two-stage neural reward model that first learns the hidden direction

θ^*

from reward-weighted samples and then fits the readout layer by weighted ridge regression. Exponential reward weighting changes the Hermite signal available to the first layer; for any feature-learning temperature

β_1

above a dimension-free

O(1)

threshold, a constant fraction of neurons recover the hidden direction, with weak-recovery complexity governed by the generative exponent. After feature recovery, we derive tilted-policy value-gap bounds for an idealized label-weighted fit with weights

e^{y/β_2}

and a more practical surrogate-weighted fit with weights

e^{r_{a_0}(x)/β_2}

. Keeping the

β_2

-dependence explicit yields an admissible set of deployment temperatures, balancing the gain from lowering

β_2

against the learning cost amplified by exponential weighting; in the surrogate-weighted case, proxy-dependent factors shrink this admissible set.

Rei Higuchi, Ryotaro Kawata, Akifumi Wachi +3

The University of Tokyo · RIKEN AIP · LY Corporation

Reward Modeling Representation Learning Single-Index Models KL-Regularized RL Policy Optimization Policy Learning

May 21, 2026cs.LG

Two is better than one: A Collapse-free Multi-Reward RLIF Training Framework

Reinforcement learning with verifiable rewards (RLVR) has substantially improved the reasoning ability of LLMs, but often depends on external supervision from human annotations or gold-standard solutions. Reinforcement learning from internal feedback (RLIF) has recently emerged as a scalable unsupervised alternative, using signals extracted from the model itself. However, existing RLIF methods typically rely on a single internal reward, which can lead to reward hacking, entropy collapse, and degraded reasoning structure. We propose a multi-reward RLIF framework that decomposes the training signal into two complementary components: an answer-level reward based on cluster voting and a completion-level reward based on token-wise self-certainty. To combine these signals robustly, we apply GDPO-based normalization to reduce reward-scale imbalance. We further introduce KL-Cov regularization, which targets low-entropy token distributions responsible for disproportionate entropy reduction, preserving exploration and preventing late-stage collapse. Across mathematical reasoning and code-generation benchmarks, our method improves stability and robustness over prior unsupervised RL approaches, while achieving performance close to supervised RLVR methods. These results show that complementary internal rewards, combined with targeted regularization, can support stable long-horizon reasoning without relying on external ground-truth supervision. Code will be released soon.

Shourov Joarder, Diganta Sikdar, Ahsan Habib Akash +2

Bangladesh University of Engineering and Technology, Bangladesh · West Virginia University, USA · University of Aberdeen, UK +2

Multi-Objective Reinforcement Learning Intrinsic Reward Methods Reinforcement Learning KL-Regularized RL RL for Language Model Reasoning Reward Design for RL

May 19, 2026cs.AI

Beyond Mode Collapse: Distribution Matching for Diverse Reasoning

On-policy reinforcement learning methods like GRPO suffer from mode collapse: they exhibit reduced solution diversity, concentrating probability mass on a single solution once discovered and ceasing exploration of alternative strategies. We show this stems from reverse KL minimization's mode-seeking behavior, which reinforces the first high-reward trajectory found rather than maintaining a distribution over multiple diverse solutions. We propose DMPO (Distribution-Matching Policy Optimization), which prevents mode collapse through principled approximation of forward KL minimization. DMPO constructs a group level target distribution over sampled trajectories proportional to their rewards, then aligns the policy distribution to this target. This provides mode-covering behavior without requiring sampling from the intractable global target distribution, enabling sustained exploration throughout training. We validate DMPO on NP-hard combinatorial optimization, where exponentially many feasible solutions exist but only a few approach optimality, an ideal testbed for evaluating exploration. DMPO achieves 43.9% Quality Ratio on text-based NP-Bench (vs. GRPO's 40.1%) and 43.1% on vision-based NP-Bench (vs. 38.4%), demonstrating 9% and 12% relative improvements respectively. These gains generalize to mathematical reasoning (+2.0%) and out-of-domain tasks (+2.3%), showing that diversity-preserving training enhances general reasoning capabilities across modalities. Our work establishes distribution matching as a practical, principled approach to preventing mode collapse in on-policy RL, with consistent quality improvements demonstrating sustained exploration across diverse reasoning tasks.

Xiaozhe Li, Yang Li, Xinyu Fang +10

1Tongji University, China · 6Independent · 2Shanghai AI Laboratory, China +3

KL-Regularized RL RL for Language Model Reasoning RL Exploration Mode Collapse

May 17, 2026cs.LG

Reasoning Portability: Guiding Continual Learning for MLLMs in the RLVR Era

Vision-Language Models in Continual Learning (VLM-CL) aim to continuously adapt to new multimodal tasks while retaining prior knowledge. The emerging paradigm that couples Multimodal Large Language Models (MLLMs) with Reinforcement Learning with Verifiable Rewards (RLVR) calls for a new pattern to guide continual adaptation. Advances in reasoning capability now make it feasible to impose constraints at the reasoning level. We formalize portability, a sample-level measure of how reusable the previous policy's behavior is on a new task, and empirically show that reasoning-level signals remain reliable on out-of-distribution samples while answer-level signals do not. We instantiate this as Reasoning Portability (RP) and propose Reasoning-based Dynamic Balance Continual Learning (RDB-CL), which modulates the per-sample Kullback-Leibler regularization in RLVR according to RP: a tight anchor preserves reusable reasoning on high-RP samples, while a relaxed anchor on low-RP samples permits exploration of new reasoning pathways. Experiments show that RDB-CL consistently outperforms baselines, improving Last accuracy by +12.0% over the vanilla RLVR baseline.

Qiuhe Hong, Yuyang Liu, Shuo Yang +3

1Shenzhen Graduate School of Peking University · Centre for Artificial Intelligence and Robotics, HKISI, CAS · 3Peng Cheng Laboratory

KL-Regularized RL Continual Learning Continual Learning for VLMs

May 15, 2026cs.LG

SAGE: Shaping Anchors for Guided Exploration in RLVR of LLMs

Recent studies observe that reinforcement learning with verifiable rewards (RLVR) reliably improves pass@1 on reasoning tasks, yet often fails to yield comparable gains in pass@k, raising the question of whether RLVR genuinely enables large language models to acquire novel reasoning abilities or merely enhances the efficiency of sampling reasoning modes already present in the base model. Prior analyses largely support the latter view, attributing this limitation to structural properties of standard RLVR objectives that result in insufficient exploration pressure. In this work, we argue that a central structural constraint arises from reverse-KL regularization, which stabilizes training but inherently anchors the policy to the reference distribution, thereby suppressing the emergence of alternative reasoning modes. However, we show that neither removing the KL term nor replacing it with forward-KL provides a satisfactory solution, as both disrupt the efficiency-coverage trade-off by either inducing reward hacking or allocating probability mass to off-target regions. To resolve this tension, we propose SAGE, a principled framework that enables controllable empirical support expansion by reshaping the reverse-KL anchor distribution itself through a guide function q(x,y), achieving consistent improvements in both pass@1 and pass@k across challenging mathematical reasoning benchmarks. Our code is available at https://github.com/tally0818/SAGE.

Chanuk Lee, Minki Kang, Sung Ju Hwang

KAIST

KL-Regularized RL RL for Language Model Reasoning Mathematical Reasoning Reinforcement Learning with Verifiable Rewards

May 13, 2026cs.LG

Offline Two-Player Zero-Sum Markov Games with KL Regularization

We study the problem of learning Nash equilibria in offline two-player zero-sum Markov games. While existing approaches often rely on explicit pessimism to address distribution shift, we show that KL regularization alone suffices to stabilize learning and guarantee convergence. We first introduce Regularized Offline Sequential Equilibrium (ROSE), a theoretical framework that achieves a fast

\widetilde{\mathcal{O}}(1/n)

convergence rate under \textit{unilateral concentrability}, improving over the standard

\widetilde{\mathcal{O}}(1/\sqrt{n})

rates in unregularized settings. We then propose Sequential Offline Self-play Mirror Descent (SOS-MD), a practical model-free algorithm based on least-squares value estimation and iterative self-play updates. We prove that the last iterate of SOS-MD attains the same

\widetilde{\mathcal{O}}(1/n)

statistical rate up to a vanishing optimization error of order

\widetilde{\mathcal{O}}(1/\sqrt{T})

in the number of self-play iterations

T

.

Claire Chen, Yuheng Zhang, Xinyu Liu +3

1California Institute of Technology. · University of Illinois Urbana-Champaign. · University of Virginia. +2

Nash Equilibrium Reinforcement Learning Self-Play RL KL-Regularized RL Game Theory Zero-Sum Games+3

May 12, 2026cs.LG

The tractability landscape of diffusion alignment: regularization, rewards, and computational primitives

Inference-time reward alignment asks how to turn a pre-trained diffusion model with base law

p

into a sampler that favors a reward

r

while remaining close to

p

. Since there is no canonical distributional distance for this closeness constraint, different choices lead to different "reward-aligned" laws and, just as importantly, different algorithmic problems. We develop a primitive-based approach to reward alignment: rather than assuming arbitrary reward-aligned laws can be sampled, we ask which simple algorithmic primitives suffice to implement alignment for non-trivial reward classes. If closeness is measured in KL distance, the target law is

q(x) \propto p(x) \exp(λ^{-1}r(x))

. For this setting, we show that linear exponential tilts of the form

q(x)\propto p(x)\exp(\langle θ, x \rangle)

-- which according to recent work [MRR26] can be efficiently sampled from -- are a sufficient primitive for aligning to a very broad class of convex low-dimensional rewards. If closeness is measured in Wasserstein distance, the corresponding primitive is a proximal transport oracle: given

x

, solve

\mbox{argmax}_y \{r(y)- λc(x,y)\}

. This oracle can be efficiently implemented for concave or low-dimensional Lipschitz rewards

r(x)=f(Ax)

. Together, these results illustrate that the choice of distribution distance for alignment affects the computational primitive and the tractable reward class.

Ankur Moitra, Andrej Risteski, Dhruv Rohatgi

Diffusion Model Alignment KL-Regularized RL

May 11, 2026cs.AI

expo: Exploration-prioritized policy optimization via adaptive kl regulation and gaussian curriculum sampling

Reinforcement Learning with Verifiable Rewards (RLVR) has become the standard paradigm for LLM mathematical reasoning, where Group Relative Policy Optimization (GRPO) serves as the mainstream algorithm. We point out two understudied inefficiencies existing in GRPO. First, the fixed KL penalty coefficient overly restricts policy exploration at stages where the model requires significant deviation from the reference policy. Second, uniform sampling of training questions ignores that moderately difficult problems provide the most informative gradient signals for optimization. We propose Exploration-Prioritized Policy Optimization (EXPO) with two lightweight plug-in modules. The Accuracy-Conditioned KL Scaling (AKL) dynamically adjusts KL regularization strength through a smooth nonlinear function of batch average accuracy, relaxing the penalty when the model underperforms and strengthening it when the model achieves good results. The Gaussian Curriculum Sampling (GCS) assigns sampling weights to questions following a Gaussian distribution centered at moderate accuracy around 0.5, focusing training on the model's learning frontier. We conduct extensive experiments on DeepSeek-R1-Distill-Qwen-1.5B and Qwen3-8B-Base over six mathematical reasoning benchmarks. The results show EXPO steadily surpasses vanilla GRPO. It obtains an absolute gain of 13.34 on AIME 2025 pass@32, rising from 63.33 percent to 76.67 percent, and achieves an average pass@32 improvement of 2.66 on the 8B model. The much larger performance gains on pass@32 compared with pass@1 demonstrate that EXPO effectively enlarges the model's exploration boundary under a fixed inference cost budget.

Mingxiong Lin, Zhangquan Gong, Maowen Tang +6

OPPO AI Center

Reinforcement Learning KL-Regularized RL RL for Language Model Reasoning Group Relative Policy Optimization Curriculum RL RL Exploration+2

May 9, 2026cs.LG

Fast Rates for Offline Contextual Bandits with Forward-KL Regularization under Single-Policy Concentrability

\emph{Kullback-Leibler} (KL) regularization is ubiquitous in reinforcement learning algorithms in the form of \emph{reverse} or \emph{forward} KL. Recent studies have demonstrated

ε^{-1}

-type fast rates for decision making under reverse KL regularization, in contrast to the standard

ε^{-2}

-type sample complexity. However, for forward-KL-regularized objectives, existing statistical analyses are either not applicable or result in

\tilde{O}(ε^{-2})

slow rates. We take the first step towards addressing this problem via a streamlined analysis of forward-KL-regularized offline CBs. We give the first

\tilde{O}(ε^{-1})

upper bounds in tabular and general function approximation settings, both under notions of \emph{single-policy concentrability}. In particular, our convex-analytical pipeline unifies these settings by exploiting the pessimism principle in a novel way and completely bypasses the proof routines in previous works based on the mean value theorem, which might be of independent interest. Moreover, we provide rate-optimal lower bounds, manifesting the tightness of our upper bounds in terms of statistical rates. Our lower bounds also demonstrate that the forward-KL-regularized sample complexity recovers the unregularized slow rate in the low-regularization regime, similarly to the reverse-KL regularization.

Qingyue Zhao, Kaixuan Ji, Heyang Zhao +1

Department of Computer Science, University of California, Los Angeles, CA 90095, USA

KL-Regularized RL Contextual Bandits

May 8, 2026cs.LG

Theoretical Limits of Language Model Alignment

Language model (LM) alignment improves model outputs to reflect human preferences while preserving the capabilities of the base model. The most common alignment approaches are (i) reinforcement learning, which maximizes the expected reward under a KL-divergence constraint, and (ii) best-of-

N

alignment, which selects the highest-reward output among

N

independent samples. Despite their widespread use, the fundamental limits of reward improvement under a KL budget remain poorly understood. We characterize the information-theoretic limits of KL-regularized alignment by deriving the maximum achievable expected reward gain for a fixed KL-divergence budget. Our first result provides a closed-form expression for the optimal reward improvement, governed by a Jeffreys divergence term rather than the

\sqrt{\texttt{KL}}

used in prior analyses. We further reformulate this expression as a covariance under the base model, yielding a practical estimator that predicts achievable alignment gains from base model samples alone. We extend our analysis to the proxy reward setting, showing that the gap between ideal and proxy alignment (reward hacking) grows with the magnitude of reward error and when the KL penalty factor decreases. We then prove that reward ensembling mitigates reward hacking, providing a theoretical justification for this technique used in practice. Empirically, we compute the KL-reward Pareto frontier for two tasks for LMs, safety and summarization, and show that best-of-

N

closely approaches the theoretical limit, while PPO and GRPO remain substantially suboptimal. Our theoretical results shed light on several empirically observed phenomena in the alignment literature and suggest that algorithmic improvements are needed to achieve optimal alignment without high inference costs.

Lucas Monteiro Paes, Natalie Mackraz, Barry-John Theobald +1

Apple

Reward Hacking LLM Alignment KL-Regularized RL Preference Alignment

May 7, 2026cs.AI

Market-Alignment Risk in Pricing Agents: Trace Diagnostics and Trace-Prior RL under Hidden Competitor State

Outcome metrics can certify the wrong behavior. We study this failure in a two-hotel revenue-management simulator where Hotel A trains an agent against a fixed rule-based revenue-management competitor, Hotel B. A standard learning agent can obtain near-reference revenue per available room (RevPAR) while failing to learn market-like yield management: it sells too aggressively, undercuts, or collapses to modal price buckets. We diagnose this as a Goodhart-style failure under partial observability. Hotel A cannot observe the competitor's remaining inventory, booking curve, or pricing rule, so the same Hotel A-visible state maps to multiple plausible Hotel B prices. Deterministic value-based RL and deterministic copying collapse this unresolved uncertainty into shortcut behavior. We introduce a trace-level diagnostic protocol using RevPAR, occupancy, ADR, full price-bucket distributions, L1/JS distances, and seed-level confidence intervals. The verified repair is Trace-Prior RL: learn a distributional market prior from lagged market traces, then train a stochastic pricing policy with a RevPAR reward and a KL penalty to the learned prior. The final policy matches Hotel B's RevPAR, occupancy, ADR, and price distribution within seed-level uncertainty, while still optimizing Hotel A's own reward. We argue that the contribution is not a new optimizer and not a hotel-pricing leaderboard, but a reproducible failure-and-repair recipe for agentic systems where scalar rewards are easy to game and the intended behavior is only visible in traces. A key finding is that higher exact action accuracy can worsen aggregate trace alignment when the target is distributional.

Peiying Zhu, Sidi Chang

Blossom AI · Blossom AI Labs

Reward Hacking Reinforcement Learning Partially Observable RL KL-Regularized RL Dynamic Pricing