Constrained RL

RL: Reinforcement Learning

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22 papers in the last four weeks, up 175% on the four weeks before. 0.2% of all new papers.

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Latest papers 143

May 26, 2026cs.LG

When Does Deep RL Beat Calibrated Baselines? A Benchmark Study on Adaptive Resource Control

A properly calibrated rule-based autoscaler can beat every one of six mainstream deep reinforcement learning (DRL) algorithms on cost across every workload we test - so when, if ever, does DRL actually help? We study this in RLScale-Bench, a reproducible benchmark and evaluation protocol for DRL on adaptive resource control, where an agent allocates compute to a dynamic workload under cost and service-level constraints. We evaluate PPO, DQN, A2C, SAC, TD3, and DDPG under matched architectures, training budgets, and reward functions against a calibrated rule-based baseline across six workload patterns and five seeds (240 runs), instantiate the benchmark on Kubernetes Horizontal Pod Autoscaling, and probe distribution-shift generalization. Three findings challenge common assumptions: (i) the calibrated controller achieves the lowest cost on all six workloads, though it trails the best RL agents on bursty and flash traffic; (ii) discrete-action algorithms outperform continuous-action ones by one to two orders of magnitude in constraint violations due to action-space mismatch; and (iii) no single algorithm dominates across workloads, with rankings shifting by up to four positions. The bottleneck in RL-based resource control is not algorithm selection but baseline calibration, reward engineering, and realistic evaluation protocols.

Guilin Zhang, Chuanyi Sun, Kai Zhao +3

The George Washington University, Washington, DC, USA

RL Control RL Benchmarks Constrained RL Online Resource Allocation

May 24, 2026stat.ML

Counterfactually Safe Reinforcement Learning

Reinforcement learning algorithms are generally designed to maximize the expected return across a population. However, a policy that is optimal on average may be suboptimal for certain individuals, leading to potential safety concerns. To address this, we first formalize the notion of individual harm from a counterfactual perspective and define harm as the event in which a chosen action results in a strictly worse outcome than a baseline alternative. We then propose a general two-stage procedure for learning policies that maximize the expected return while accounting for individual harm. We further establish the finite-sample properties of the learned policy, derive an upper bound on its sub-optimality gap, and show that the harm rate remains well-controlled. Numerical experiments on both simulated and real-world datasets demonstrate the effectiveness of the proposed approach.

Jingyi Li, Peng Wu, Chengchun Shi

Department of Statistics and Data Science, National University of Singapore · School of Mathematics and Statistics, Beijing Technology and Business University · Department of Statistics, London School of Economics and Political Science

Constrained RL Safe RL

May 24, 2026cs.LG

Reinforcement Learning with a Bilevel World-Model Architecture for Scan-Order Optimisation in Laser Directed Energy Deposition

Scan-order design in laser directed energy deposition (LDED) is a delayed, path-dependent thermo-mechanical decision problem, because sequence quality becomes observable only after the complete deposition and cooling cycle. This work formulates LDED scan-order optimisation as a finite-horizon, permutation-constrained reinforcement-learning problem and develops a bilevel finite-element-teacher-labelled AI workflow. A surrogate-assisted teacher-guided optimisation loop learns the Abaqus-labelled response landscape and provides a tractable terminal-reward environment for policy training. A frozen Maskable Proximal Policy Optimization (MaskablePPO) policy is then used to generate legal scan-order candidates, which are independently validated through Abaqus thermo-mechanical simulations. The results show bounded, N-dependent policy-generation value rather than record-level dominance over the mature surrogate-assisted optimiser. The strongest scan orders are obtained by the teacher-guided surrogate loop, whereas PPO autonomously reaches competitive regions of the native response landscape, with stronger rank concentration at smaller track counts and a clear reliability boundary at longer horizons. The teacher-labelled landscape further supports a physically gated lexicographic reward hierarchy in which warpage admissibility is the primary constraint, plastic strain acts as a safety filter and residual-stress-related improvement is pursued conditionally within the admissible region. Validated sequences also reveal an interpretable scale-separated ordering tendency that combines global spatial dispersion with local structured grouping. This workflow provides a route from fixed scan-rule selection toward finite-element-teacher-validated policy generation, while preserving independent finite-element validation as the final physical gate.

Xian Wu, Haoran Li, Yuanqi Chu +2

aCollege of Engineering, Design and Physical Sciences, Brunel University London, Uxbridge, UB8 3PH, United Kingdom · bThe State Key Laboratory of Management and Control for Complex Systems, Institute of Automation, Chinese Academy of Sciences, Beijing, 100190, China

May 23, 2026cs.LG

A Unified Python Framework for Direct PPO-based Control of AHUs with Economizer Logic and CO2-Constrained Ventilation

Optimizing HVAC (Heating, Ventilation and Air Conditioning) can enhance a building's energy efficiency while providing comfort levels for its occupants. Using conventional control systems to maintain HVAC functions is often difficult because of the nonlinear characteristics of a building envelope as it experiences stochastic load variations over time. This paper presents a new approach to optimizing HVAC systems through the use of Deep Reinforcement Learning (DRL) algorithms and the Proximal Policy Optimization (PPO) algorithm implemented in a custom Python performance environment. The DRL system uses a second order resistor-capacitor thermal model and an integrated dynamic mass balance of CO2 to replicate the complex physics associated with buildings. One major innovation of this study is a "Hierarchical Flow Logic," which provides the means to ensure that indoor air quality (IAQ) is maintained by overriding the accepted actions of the agent that cause CO2 to exceed 1000 ppm. In addition, an enthalpy-based economiser is used to create free cooling from the outdoor environment. The experimental data shows that compared to PID controllers tuned by GA or traditional On-Off controls, a PPO agent has better temperature stability and energy efficiency overall. An end-to-end pipeline provides an avenue for robust and generalized solutions to help implement smart building energy management within the context of real hardware implementation.

Erfan Haghighat Damavandi, Davide Papurello, Mahdi Alibeigi +3

a Research and Development Department Owtana Tech- Turin, Italy · b Department of Energy Politecnico di Torino- Turin, Italy · c Department of Energy University of Tehran- Tehran, Iran +1

RL Control Constrained RL Building Energy Management Feedback Control Heating, Ventilation, and Air Conditioning Control

May 20, 2026cs.LG

FedCritic: Serverless Federated Critic Learning-based Resource Allocation for Multi-Cell OFDMA in 6G

In sixth-generation (6G) ultra-dense networks, aggressive frequency reuse amplifies inter-cell interference (ICI), making multi-cell orthogonal frequency-division multiple access (OFDMA) scheduling and power control strongly coupled across neighboring cells. We study distributed downlink resource management -- joint subcarrier scheduling and power allocation -- under interference coupling and long-term per-user quality-of-service (QoS) minimum-rate constraints. By using virtual-queue deficit weights to enforce long-term QoS, we develop FedCritic, a serverless federated multi-agent actor-critic framework with decentralized execution. Unlike centralized training with decentralized execution (CTDE) approaches that require centralized critic learning and joint trajectory aggregation, FedCritic federates the critic through lightweight gossip-based parameter averaging over the interference graph, enabling stable value estimation without a central coordinator while keeping policies local. Simulations in an interference-rich reuse-1 setting show that FedCritic improves mean signal-to-interference-plus-noise ratio (SINR) and cell-edge rate, increases network-wide average sum-rate and fairness relative to non-coordinated and CTDE baselines, and achieves more stable training with lower coordination overhead.

Amin Farajzadeh, Melike Erol-Kantarci

School of Electrical Engineering and Computer Science, University of Ottawa, Ottawa, Canada

Federated RL 6G Networks Constrained RL Wireless Resource Allocation Cooperative MARL

May 20, 2026cs.LG

PREFINE: Preference-Based Implicit Reward and Cost Fine-Tuning for Safety Alignment

We address the problem of making a pre-trained reinforcement learning (RL) policy safety-aware by incorporating cost constraints without retraining it from scratch. While costs could be numerically encoded, we assume a more general setting is when costs are provided as preferences. Given a reward-optimized policy and a small dataset of preferred (low-cost) and dispreferred (high-cost) trajectories, our goal is to fine-tune the policy to generate low-cost behaviors while retaining high rewards. Unlike standard RLHF in language models, where preferences are defined over responses to the same prompt, our setting involves trajectory-level preferences in continuous control environments. We introduce PREFINE: Preference-based Implicit Reward and Cost Fine-Tuning for Safety Alignment which is a preference-based fine-tuning method that adapts Direct Preference Optimization (DPO), which is now widely used for LLM fine-tuning, to the sequential decision making setting. PREFINE constructs policy-sampled counterfactual trajectories to establish meaningful preference contrasts and jointly optimizes for reward retention and safety alignment. Empirically, PREFINE reduces constraint violations and catastrophic failures by over 60% while maintaining original reward behavior. PREFINE produces policies that achieve low-cost, high-reward performance with significantly improved data and computational efficiency compared to full offline RL or imitation learning, bridging preference alignment and safe policy adaptation in continuous domains.

Richa Verma, Bavish Kulur, Sanjay Chawla +1

TCS Research, Department of CSE, IIT Madras India · Department of Computing Science, University of Alberta Canada · Qatar Computing Research Institute, Hamad Bin Khalifa University Qatar +1

Direct Preference Optimization Constrained RL Continuous Control Safe RL RL Fine-Tuning Preference-Based RL

May 18, 2026cs.LG

Beyond Inference-Time Search: Reinforcement Learning Synthesizes Reusable Solvers

Large language models (LLMs) typically approach combinatorial optimization as an inference-time procedure, solving each instance separately through sampling, search, or repeated prompting. We ask whether reinforcement learning can instead shift part of this reasoning cost into the weights of a code LLM, so that the model synthesizes a reusable solver for an entire problem family. We study this question on Synergistic Dependency Selection (SDS), a controlled variant of constrained Quadratic Knapsack designed to expose a specific failure mode: local signals and strict feasibility constraints make greedy heuristics attractive but unreliable. Under identical scaffolding, Best-of-64 base-model sampling saturates at an approximately 28.7% gap to the global Virtual Best Solver (VBS); code audits show that the base model often retrieves Simulated Annealing templates but misimplements the Metropolis acceptance rule. We fine-tune Qwen2.5-Coder-14B-Instruct with Group Relative Policy Optimization (GRPO) using a feasibility-gated reward and light structural scaffolding. The resulting policy converges to a constraint-aware Simulated Annealing template in 99.8% of feasible SDS outputs, achieves a 5.0% gap to that VBS, and is 91 times cheaper in post-generation execution/search cost than cumulative Best-of-64 evaluation. A compile-once check shows that one best frozen solver per seed remains highly competitive when reused unchanged across the SDS test set, while an additional-domain evaluation on Job Shop Scheduling provides narrower but positive evidence that the scaffold transfers beyond SDS. Negative ablations reveal the limits of this recipe: standard stabilizers degrade performance, a soft feasibility gate fails, and results remain sensitive to reward normalization and domain-specific design choices.

Soheyl Massoudi, Gabriel Apaza, Milad Habibi +1

ETH Zürich Zürich, Switzerland · University of Maryland College Park, MD, USA

RL for Code Generation LLM-Based Program Synthesis Combinatorial Optimization Constrained RL RL for Combinatorial Optimization RL Fine-Tuning

May 15, 2026cs.LG

parallelcbf: A composable safety-filter and auditability framework for tensor-parallel reinforcement learning

While Isaac Lab provides massive parallel UAV simulation, OmniSafe and safe-control-gym provide constrained-RL benchmarks, and CBFKit provides control-barrier-function synthesis tooling, no existing framework unifies these capabilities for end-to-end safety-constrained training. ParallelCBF is the first framework to unify (i)~tensor-parallel UAV environments, (ii)~hard-gate CBF safety filters, (iii)sharded BC-to-RL pipelines, and (iv)first-class operational auditability -- pre-registration, watchdog registries, failure forensics, and dataset audits as composable APIs rather than user-implemented scripts. We release ParallelCBF v0.1.0 under Apache2.0 with a four-layer composable API, a CPU PyTorch reference implementation of a dual-barrier (squared / linear-predictive) CBF, property-based safety invariance tests across vectorized batch sizes that complete in 1.67s for the full 39-test suite, and a 31{,}415-episode behavior-cloning collection campaign whose curriculum mix, per-bucket yields, and dataset SHA-256 are auditable through the framework's own \texttt{ops} primitives. We report a representative end-to-end pipeline execution in which the framework's auditability layer halted a downstream training stage that did not meet pre-registered convergence criteria, preventing silent propagation of a degraded checkpoint -- an architectural property we argue is necessary, not merely useful, for reproducible empirical robotics research. The framework is installable via \texttt{pip install parallelcbf}; source and release artifacts are available at https://github.com/xiaoyang-123-cell/ParallelCBF.

Yijun Lu, Zilei Yang, Yuyin Ma

Reinforcement Learning Control Barrier Functions Constrained RL Safety Filtering ML Reproducibility Safe RL

May 14, 2026eess.SY

Addressing Terminal Constraints in Data-Driven Demand Response Scheduling

Electrified chemical processes are incentivized by exposure to time-varying electricity markets to operate flexibly, but participating in demand response schemes can require satisfying terminal constraints over long horizons. Specifically, terminal constraints may be required when computing optimal schedules in order to preserve dynamic stability. Model-based optimization methods are computationally costly, and data-driven scheduling via reinforcement learning (RL) faces severe credit-assignment challenges. We integrate Goal-Space Planning (GSP) with Deep Deterministic Policy Gradient (DDPG), using learned temporally abstract models over discrete subgoals to propagate value across extended horizons. Using a simulated air separation benchmark, we demonstrate the proposed approach improves sample efficiency over standard DDPG while satisfying terminal storage constraints, mitigating myopic control behavior.

Maximilian Bloor, Martha White, Ehecatl Antonio del Rio Chanona +1

Sargent Centre for Process Systems Engineering, Imperial College London, London, SW7 2AZ, UK · Department of Computer Science, University of Alberta, Edmonton, AB, Canada · Department of Computing, Imperial College London, London, SW7 2AZ, UK

Hierarchical RL Credit Assignment in RL Constrained RL Data-Driven Control Demand Response Sample-Efficient RL

May 14, 2026cs.CV

CreFlow: Corrective Reflow for Sparse-Reward Embodied Video Diffusion RL

Video generation models trained on heterogeneous data with likelihood-surrogate objectives can produce visually plausible rollouts that violate physical constraints in embodied manipulation. Although reinforcement-learning post-training offers a natural route to adapting VGMs, existing video-RL rewards often reduce each rollout to a low-level visual metric, whereas manipulation video evaluation requires logic-based verification of whether the rollout satisfies a compositional task specification. To fill this gap, we introduce a compositional constraint-based reward model for post-training embodied video generation models, which automatically formulates task requirements as a composition of Linear Temporal Logic constraints, providing faithful rewards and localized error information in generated videos. To achieve effective improvement in high-dimensional video generation using these reward signals, we further propose CreFlow, a novel online RL framework with two key designs: i) a credit-aware NFT loss that confines the RL update to reward-relevant regions, preventing perturbations to unrelated regions during post-training; and ii) a corrective reflow loss that leverages within-group positive samples as an explicit estimate of the correction direction, stabilizing and accelerating training. Experiments show that CreFlow yields reward judgments better aligned with human and simulator success labels than existing methods and improves downstream execution success by 23.8 percentage points across eight bimanual manipulation tasks.

Zhenyang Ni, Yijiang Li, Ruochen Jiao +7

Northwestern University · University of California, San Diego · University of Oxford

Video Diffusion Models Reinforcement Learning RL for Video Generation Constrained RL RL for Diffusion Models RL for Generative Models+1

May 13, 2026cs.RO

Safety-Constrained Reinforcement Learning with Post-Training Reachability Verification for Robot Navigation

Safe navigation for mobile robots demands policies that remain reliable under the high-consequence perception uncertainty of cluttered environments. Yet most existing safe reinforcement learning (RL) methods assess safety through average cumulative cost. Such metrics can mask dangerous tail-risk behaviors. To address this, we propose a framework that trains risk-sensitive policies through Conditional Value-at-Risk (CVaR) constrained optimization on an off-policy TD3 backbone and evaluates their safety margins post-training through neural network reachability verification. During training, the policy is optimized under CVaR constraints on cumulative costs, promoting sensitivity to high-cost tail outcomes rather than average behavior alone. After training, we compute action reachable sets under bounded observation uncertainty using Taylor Model analysis, yielding a safety rate metric that quantifies the proportion of evaluated states at which the policy's reachable action set remains within prescribed safety margins. A key finding is that policies trained with CVaR constraints maintain larger safety margins from obstacles across evaluated states. This makes them significantly more amenable to formal reachability verification. Experiments across ten navigation scenarios and six baselines show that our method achieves a 98.3% success rate, the highest safety verification rate among all compared methods, while revealing that average cost rankings and reachability-based safety rankings can diverge. This indicates that reachability verification captures risks which are missed by empirical cost metrics alone. We further validate our approach on a physical Clearpath Jackal robot, demonstrating successful sim-to-real transfer.

Qisong He, Xinmiao Huang, Jinwei Hu +4

University of Liverpool, Liverpool, UK. · Universit´e Grenoble Alpes, Grenoble, France.

Constrained RL Risk-Sensitive RL Safe Robot Navigation Robot Safety

May 13, 2026cs.AI

Learning Local Constraints for Reinforcement-Learned Content Generators

Constraint-based game content generators that learn local constraints from existing content, such as Wave Function Collapse (WFC), can generate visually satisfying game levels but face challenges in optimizing global properties, such as playability. On the other hand, reinforcement-learning-trained generators can optimize global properties---because such properties can easily be included in reward functions---but the results can be visually dissatisfying. In this paper, we explore ways to combine these methods. Specifically, we constrain the action space of a PCGRL generator with constraints learned by WFC, effectively allowing the PCGRL generator to achieve global properties while being forced to adhere to local constraints. To better analyze how this hybrid content generation method operates, we vary the number and type of inputs, and we test whether to randomly collapse the starting state and exclude rare patterns. While the method is sensitive to hyperparameter tuning, the best of our trained generators produce visually satisfying and playable puzzle-platform game levels---such as Lode Runner levels---with desired global properties.

Debosmita Bhaumik, Julian Togelius, Georgios N. Yannakakis +1

Institute of Digital Games, Msida, Malta · Game Innovation Lab, New York, New York, USA

Constrained Generative Modeling Constrained RL Generative Modeling Procedural Content Generation RL for Generative Models

May 13, 2026cs.LG

Safe Continual Reinforcement Learning under Nonstationarity via Adaptive Safety Constraints

Safe reinforcement learning in nonstationary environments requires safety mechanisms that adapt as environmental conditions change. Standard safe reinforcement learning methods often assume fixed constraints or stable environmental conditions, which can become inadequate under distribution shift. We propose LILAC+, a framework for safe continual reinforcement learning under nonstationarity that combines three adaptive safety mechanisms: context-based safety constraints, adaptation-speed constraints, and budget-to-state safety enforcement. Context-based constraints adjust safety requirements using inferred and predicted environmental context. Adaptation-speed constraints tighten safety requirements when the rate of environmental change exceeds the agent's ability to adapt safely. Budget-to-state enforcement converts cumulative safety requirements into local state-level control constraints that can be enforced at decision time. Together, these mechanisms provide a unified approach for proactive and reactive safety adaptation in continual reinforcement learning. We evaluate the framework in simulated driving environments under stationary, seen nonstationary, and unseen nonstationary conditions. The results show that adaptive safety constraints substantially reduce safety violations under distribution shift while maintaining competitive task performance compared with unconstrained and fixed-constraint baselines. These findings suggest that safe continual reinforcement learning requires adaptive constraint mechanisms that respond not only to current state information but also to predicted environmental context, adaptation demand, and remaining safety budget.

Timofey Tomashevskiy

McMaster Centre for Software Certification Department of Computing and Software McMaster University, Canada

Non-Stationary RL Reinforcement Learning Constrained RL Safe RL Continual RL

May 13, 2026cs.LG

From Cumulative Constraints to Adaptive Runtime Safety Control for Nonstationary Reinforcement Learning

Safety in reinforcement learning is often specified through cumulative cost constraints, but these trajectory-level guarantees do not directly prevent unsafe individual decisions, especially under nonstationarity. In continual and nonstationary settings, the difficulty is amplified because the risk associated with the same action can vary across contexts, while a fixed state-level threshold may be either too conservative or too weak. We propose Constraint Projection Safety Shield (CPSS), a runtime mechanism that converts a cumulative safety budget into adaptive state-level control constraints during execution. CPSS tracks the remaining safety budget, projects it into a time-varying admissible risk threshold, and filters policy actions whose predicted safety cost exceeds the active threshold. The threshold is adjusted online using contextual signals so that enforcement becomes stricter in more demanding or rapidly changing regimes and less restrictive when the available safety budget is sufficient. We analyze the resulting shielded policy and show that the mechanism guarantees per-state threshold satisfaction for executed actions, induces finite-horizon cumulative cost bounds, and yields a performance degradation bound in terms of intervention frequency and per-step reward distortion. We evaluate CPSS in nonstationary highway merging scenarios using highway-env. Across multiple seeds, CPSS substantially reduces proximity-based safety violations and increases separation margins while intervening selectively rather than dominating the learned policy. These results support adaptive budget-to-threshold projection as a practical way to transform cumulative safety specifications into effective local safety control for continual reinforcement learning systems.

Timofey Tomashevskiy

McMaster Centre for Software Certification Department of Computing and Software McMaster University, Canada

Non-Stationary RL Constrained RL Safe RL

May 12, 2026stat.ML

Optimal Policy Learning under Budget and Coverage Constraints

We study optimal policy learning under combined budget and minimum coverage constraints. We show that the problem admits a knapsack-type structure and that the optimal policy can be characterized by an affine threshold rule involving both budget and coverage shadow prices. We establish that the linear programming relaxation of the combinatorial solution has an O(1) integrality gap, implying asymptotic equivalence with the optimal discrete allocation. Building on this result, we analyze two implementable approaches: a Greedy-Lagrangian (GLC) and a rank-and-cut (RC) algorithm. We show that the GLC closely approximates the optimal solution and achieves near-optimal performance in finite samples. By contrast, RC is approximately optimal whenever the coverage constraint is slack or costs are homogeneous, while misallocation arises only when cost heterogeneity interacts with a binding coverage constraint. Monte Carlo evidence supports these findings.

Giovanni Cerulli

CNR-IRCrES · National Research Council of Italy · Research Institute on Sustainable Economic Growth

Policy Optimization Combinatorial Optimization Constrained RL Constrained Optimization

May 12, 2026cs.LG

Stochastic Minimum-Cost Reach-Avoid Reinforcement Learning

We study stochastic minimum-cost reach-avoid reinforcement learning, where an agent must satisfy a reach-avoid specification with probability at least

p

while minimizing expected cumulative costs in stochastic environments. Existing safe and constrained reinforcement learning methods typically fail to jointly enforce probabilistic reach-avoid constraints and optimize cost in the learning setting in stochastic environments. To address this challenge, we introduce reach-avoid probability certificates (RAPCs), which identify states from which stochastic reach-avoid constraints are satisfiable. Building on RAPCs, we develop a contraction-based Bellman formulation that serves as a principled surrogate for integrating reach-avoid considerations into reinforcement learning, enabling cost optimization under probabilistic constraints. We establish almost sure convergence of the proposed algorithms to locally optimal policies with respect to the resulting objective. Experiments in the MuJoCo simulator demonstrate improved cost performance and consistently higher reach-avoid satisfaction rates.

Jingduo Pan, Taoran Wu, Yiling Xue +1

Key Laboratory of System Software (Chinese Academy of Sciences), Institute of Software, Chinese Academy of Sciences, Beijing, China · University of Chinese Academy of Sciences, Beijing, China · School of Advanced Interdisciplinary Sciences, University of Chinese Academy of Sciences, Beijing, China

Constrained RL Safe RL

May 12, 2026cs.LG

Augmented Lagrangian Method for Last-Iterate Convergence for Constrained MDPs

We study policy optimization for infinite-horizon, discounted constrained Markov decision processes (CMDPs). While existing theoretical guarantees typically hold for the mixture policy, deploying such a policy is computationally and memory intensive. This leads to a practical mismatch where a single (last-iterate) policy must be deployed. Recent theoretical works have thus focused on proving last-iterate convergence, but are largely limited to the tabular setting or to algorithmic variants that are rarely used in practice. To address this, we use the classic inexact augmented Lagrangian (

\texttt{AL}

) method from constrained optimization, and propose a general framework with provable last-iterate convergence for CMDPs. We first focus on the tabular setting and propose to solve the

\texttt{AL}

sub-problem with projected Q-ascent (

\texttt{PQA}

). Combining the theoretical guarantees of

\texttt{PQA}

and the standard

\texttt{AL}

analysis enables us to establish global last-iterate convergence. We generalize these results to handle log-linear policies, and demonstrate that an efficient, projected variant of

\texttt{PQA}

can achieve last-iterate convergence with comparable guarantees as prior work. Finally, we demonstrate that our framework scales to complex non-linear policies, and evaluate it on continuous control tasks.

Michael Lu, Max Qiushi Lin, Mo Chen +1

Simon Fraser University

Markov Decision Processes Last-Iterate Convergence Policy Optimization Constrained RL Convergence Analysis Augmented Lagrangian Method+1

May 12, 2026cs.LG

Learning Weakly Communicating Average-Reward CMDPs: Strong Duality and Improved Regret

We study infinite-horizon average-reward constrained Markov decision processes (CMDPs) under the weakly communicating assumption. Our contributions are twofold. First, we establish strong duality for weakly communicating average-reward CMDPs over stationary policies with finite state and action spaces. Despite the absence of a linear programming formulation and the resulting nonconvexity under the weakly communicating setting, we show that strong duality still holds by carefully exploiting the geometric structure of the occupation measure set. Second, building on this result, we propose a primal--dual clipped value iteration algorithm for learning weakly communicating average-reward linear CMDPs. Our algorithm achieves regret and constraint violation bounds of

\widetilde{\mathcal{O}}(T^{2/3})

, improving upon the best known bounds, where

T

denotes the number of interactions. Our approach extends clipped value iteration to the constrained setting and adapts it to a finite-horizon approximation, which stabilizes the dual variable and is crucial for achieving improved regret bounds. To analyze this, we develop a novel approach based on strong duality that enables the decomposition of the composite Lagrangian regret into separate bounds on regret and constraint violation.

Kihyun Yu, Beomhan Baek, Dabeen Lee

1KAIST · 2Seoul National University

Regret Minimization in RL Markov Decision Processes Reinforcement Learning Average-Reward RL Constrained RL

May 12, 2026cs.LG

Primal-Dual Policy Optimization for Linear CMDPs with Adversarial Losses

Existing work on linear constrained Markov decision processes (CMDPs) has primarily focused on stochastic settings, where the losses and costs are either fixed or drawn from fixed distributions. However, such formulations are inherently vulnerable to adversarially changing environments. To overcome this limitation, we propose a primal-dual policy optimization algorithm for online finite-horizon {adversarial} linear CMDPs, where the losses are adversarially chosen under full-information feedback and the costs are stochastic under bandit feedback. Our algorithm is the \emph{first} to achieve sublinear regret and constraint violation bounds in this setting, both bounded by

\widetilde{\mathcal{O}}(K^{3/4})

, where

K

denotes the number of episodes. The algorithm introduces and runs with a new class of policies, which we call weighted LogSumExp softmax policies, designed to adapt to adversarially chosen loss functions. Our main result stems from the following key contributions: (i) a new covering number argument for the weighted LogSumExp softmax policies, and (ii) two novel algorithmic components -- periodic policy mixing and a regularized dual update -- which allow us to effectively control both the covering number and the dual variable. We also report numerical results that validate our theoretical findings on the performance of the algorithm.

Kihyun Yu, Seoungbin Bae, Dabeen Lee

Department of Industrial and Systems Engineering KAIST · Department of Mathematical Sciences Seoul National University · Research Institute of Mathematics, Seoul National University; Interdisciplinary Program in Artificial Intelligence, Seoul National University; Korea Institute for Advanced Study

Primal-Dual Optimization Markov Decision Processes Policy Optimization Constrained RL Constrained Optimization

May 10, 2026cs.AI

Beyond ESG Scores: Learning Dynamic Constraints for Sequential Portfolio Optimization

ESG-aware portfolio optimization is increasingly important for sustainable capital allocation, yet most learning-based methods still operationalize ESG by appending static scores to the policy observation or reward. This creates a mismatch for sequential control: ESG scores are noisy, provider-dependent, low-frequency, and temporally misaligned with sequential portfolio decisions, while financial evidence suggests that ESG is better treated as a portfolio preference, risk-exposure, or hedge dimension than as a robust alpha factor. We propose to impose ESG constraints without modifying the financial policy's observation or reward, using a Multimodal Action-Conditioned Constraint Field (MACF) that learns mechanism-specific ESG costs from point-in-time multimodal evidence and contemplated portfolio transitions. We then introduce MACF-X, a family of optimizer-specific adapters that converts MACF costs and uncertainties into native constrained-optimization interfaces through a shared slack- and uncertainty-aware pressure layer. Across multiple constraint-integration interfaces, MACF-X reduces tail ESG budget pressure while maintaining competitive financial performance. Ablations show that this improvement depends on dynamic evidence inputs and three-head decomposition, while static ESG-score proxies are nearly indistinguishable from score-shuffled noise baselines.

Xin Li, Yan Ke, Longbing Cao

Macquarie University · The University of Queensland

Constrained RL Constrained Optimization Portfolio Optimization Finance

May 9, 2026cs.RO

Constraint-Aware Diffusion Priors for High-Fidelity and Versatile Quadruped Locomotion

Reinforcement learning combined with imitation learning has significantly advanced biomimetic quadrupedal locomotion. However, scaling these frameworks to massive, multi-source datasets exposes fundamental bottlenecks. First, traditional GAN-based discriminators are prone to mode collapse, struggling to capture diverse motion distributions from uncurated datasets. Second, existing kinematic priors suffer from out-of-distribution (OOD) tracking conflicts, leading to severe unintended heading drifts during complex maneuvers. Furthermore, deploying unconstrained priors to physical hardware poses critical safety risks by disregarding actuator dynamics. To overcome these challenges, we propose Diff-CAST (Diffusion-guided Constraint-Aware Symmetric Tracking), a novel motion prior framework leveraging the multi-modal distribution modeling capabilities of diffusion models for stylistic rewards. Diff-CAST effectively replaces traditional GAN discriminators, unlocking robust data scaling on heterogeneous collections. To ensure high-fidelity intent execution and reliable real-world deployment, we introduce a comprehensive Sim2Real architecture integrating Symmetric Augmented Command Conditioning (SACC) for drift-free tracking, and Constrained RL for hardware safety. Experiments on a quadruped demonstrate that Diff-CAST mitigates mode collapse, enables seamless transitions between diverse skills, and ensures robust, hardware-compliant locomotion.

Jianhui Chen, Ruixin Zhan, Liu Liu +2

Amap, Alibaba Group

Sim-to-Real Transfer Constrained RL Robot Motion Generation RL for Legged Locomotion Robot Imitation Learning Quadruped Locomotion

May 7, 2026cs.AI

Multi-Objective Constraint Inference using Inverse reinforcement learning

Constraint inference is widely considered essential to align reinforcement learning agents with safety boundaries and operational guidelines by observing expert demonstrations. However, existing approaches typically assume homogeneous demonstrations (i.e., generated by a single expert or multiple experts with identical objectives). They also have limited ability to capture individual preferences and often suffer from computational inefficiencies. In this paper, we introduce Multi-Objective Constraint Inference (MOCI), a novel framework designed to jointly extract shared constraints and individual preferences from heterogeneous expert trajectories, where multiple experts pursue different objectives. MOCI effectively models and learns from diverse, and potentially conflicting, behaviors. Empirical evaluations demonstrate that MOCI significantly outperforms existing baselines, achieving improved predictive performance, and maintaining competitive computational efficiency on a standard grid-world benchmark. These results establish MOCI as an accurate, flexible, and computationally practical approach for real-world constraint inference and preference learning tasks.

Syed Ihtesham Hussain Shah, Floris den Hengst, Aneta Lisowska +1

Faculty of Sciences Vrije Universiteit Amsterdam

Reinforcement Learning Constrained RL Preference-Based RL

May 7, 2026cs.LG

A Unified Pair-GRPO Family: From Implicit to Explicit Preference Constraints for Stable and General RL Alignment

Large language model (LLM) alignment via reinforcement learning from human preferences (RLHF) suffers from unstable policy updates, ambiguous gradient directions, poor interpretability, and high gradient variance in mainstream pairwise preference learning paradigms. To systematically address these limitations, we establish a unified theoretical framework for preference-based RL optimization centered on the Pair-GRPO family, comprising two tightly coupled variants: Soft-Pair-GRPO and Hard-Pair-GRPO. Soft-Pair-GRPO is a minimal modification of Group Relative Policy Optimization (GRPO) that replaces group-normalized scalar rewards with binary pairwise preference rewards, retaining GRPO's clipped surrogate and KL-regularized structure. We prove a critical gradient equivalence theorem: under first-order Taylor expansion around the current policy, Soft-Pair-GRPO's gradient is a positive scalar multiple of standard GRPO's gradient, explaining its empirical stability despite discarding continuous reward magnitudes. Building on this foundation, we propose Hard-Pair-GRPO, an advanced variant introducing explicit local probability constraints and constrained KL-fitting optimization to further suppress gradient noise and global policy drift. We provide comprehensive theoretical guarantees for both variants--including monotonic policy improvement, deterministic gradient direction, gradient-variance reduction, and dynamic step-size convergence. Extensive experiments on standard LLM alignment benchmarks (HH-RLHF,UltraFeedback) and the MuJoCo continuous control task HalfCheetah-v4 demonstrate that our Pair-GRPO family consistently outperforms state-of-the-art baselines in alignment quality, human preference win rate, training stability, and generalization to general reinforcement learning. Ablation studies validate the critical contributions of each core component.

Hao Yu

Department of Automation, Tsinghua University

Pairwise Preference Learning LLM Alignment Group Relative Policy Optimization Constrained RL RL Post-Training Preference-Based RL

May 5, 2026cs.LG

Constraint-Enhanced Reinforcement Learning Based on Dynamic Decoupled Spherical Radial Squashing

When deploying reinforcement learning policies to physical robots, actuator rate constraints -- hard limits on how fast each joint can move per control step -- are unavoidable. These limits vary substantially across joints due to differences in motor inertia, power bandwidth, and transmission stiffness, creating pronounced heterogeneity that existing methods fail to handle geometrically: the per-joint feasible region forms a high-dimensional box in action-increment space, yet QP projection and spherical parameterization methods impose isotropic ball-shaped constraints, exponentially under-covering the true feasible set as heterogeneity grows. This paper proposes Dynamic Decoupled Spherical Radial Squashing (DD-SRad), which resolves this mismatch by computing a position-adaptive radius independently for each actuator, achieving tight alignment with the true per-joint feasible region. DD-SRad satisfies per-step hard constraints with probability~1, preserves well-conditioned gradients throughout training, and admits exact policy gradient backpropagation with zero runtime solver overhead. MuJoCo benchmark experiments demonstrate the highest task return at zero constraint violation -- matching the unconstrained upper bound -- with 30%--50% improvement in constraint-space coverage over spherical baselines. High-fidelity IsaacLab simulations with Unitree H1 and G1 humanoid robots confirm end-to-end optimality parameterized directly from official joint specifications, validating a systematic pathway from hardware datasheets to safe deployment.

Qijun Liao, Zhaoxin Yu, Jue Yang

School of Mechanical Engineering, University of Science and Technology Beijing · Institute of Automation, Chinese Academy of Sciences

Robotic Control Constrained RL Safe RL

May 4, 2026cs.LG

Decoupled Guidance Diffusion for Adaptive Offline Safe Reinforcement Learning

Offline safe reinforcement learning often requires policies to adapt at deployment time to safety budgets that vary across episodes or change within a single episode. While diffusion-based planners enable flexible trajectory generation, existing guidance schemes often treat reward improvement and constraint satisfaction as competing gradient objectives, which can lead to unreliable safety compliance under cost limits. We reinterpret adaptive safe trajectory generation as sampling from a constrained trajectory distribution, where the budget restricts the trajectory region, and reward shapes preferences within that region. This perspective motivates Safe Decoupled Guidance Diffusion (SDGD), which conditions classifier-free guidance on the cost limit to bias sampling toward trajectories satisfying the specified limit, while using reward-gradient guidance to refine trajectories for higher return. Because direct reward guidance can increase return while also steering samples toward trajectories with higher cumulative cost, we introduce Feasible Trajectory Relabeling (FTR) to reshape reward targets and discourage such directions. We further provide a first-order sampling-time analysis showing that FTR suppresses reward-induced cost drift under a prefix-restorative alignment condition. Extensive evaluations on the DSRL benchmark show that SDGD achieves the strongest safety compliance among baselines, satisfying the constraint on 94.7% of tasks (36/38), while obtaining the highest reward among safe methods on 21 tasks.

Rufeng Chen, Zhaofan Zhang, Zhejiang Yang +2

1The Hong Kong University of Science and Technology (Guangzhou) · 2Jilin University

Diffusion-Based Planning Diffusion Guidance Constrained RL Offline RL Safe RL

May 4, 2026cs.LG

Experience Constrained Hierarchical Federated Reinforcement Learning for Large-scale UAV Teams in Hazardous Environments

Conventional federated learning assumes that greater learner participation improves training performance, by leveraging abundant, independently generated local data. However, in federated reinforcement learning (FRL) for unmanned aerial vehicle (UAV) teams in hazardous environments where experience generation is severely constrained by safety considerations, energy limitations, and mission duration, this assumption may break. This work introduces Experience-Constrained Hierarchical Federated Reinforcement Learning (EC-HFRL), a framework in which clusters act as federated learning agents, while multiple intra-cluster learners represent parallel learning resources that reuse a shared experience pool. We show that increasing participation does not necessarily improve learning performance. Instead, learning performance is strongly associated with experience reuse strategy and the dominance of key analytically identified gradient transition experiences within a cluster. In particular, minibatch size primarily determines effective replay exposure, while higher intra-cluster participation increases reuse level. Empirical results demonstrate that the performance regimes are strongly associated with the structure of the learning signal, rather than federated aggregation effects, clarifying the limited and secondary role of learner participation in experience-constrained FRL.

Qinwei Huang, Rui Zuo, Simon Khan +1

EECS Syracuse University Syracuse, USA · AFRL Air Force Research Laboratory Rome, USA

Hierarchical Federated Learning Federated RL Experience Replay Constrained RL Multi-Agent Reinforcement Learning

May 1, 2026cs.LG

Augmented Lagrangian Multiplier Network for State-wise Safety in Reinforcement Learning

Safety is a primary challenge in real-world reinforcement learning (RL). Formulating safety requirements as state-wise constraints has become a prominent paradigm. Handling state-wise constraints with the Lagrangian method requires a distinct multiplier for every state, necessitating neural networks to approximate them as a multiplier network. However, applying standard dual gradient ascent to multiplier networks induces severe training oscillations. This is because the inherent instability of dual ascent is exacerbated by network generalization -- local overshoots and delayed updates propagate to adjacent states, further amplifying policy fluctuations. Existing stabilization techniques are designed for scalar multipliers, which are inadequate for state-dependent multiplier networks. To address this challenge, we propose an augmented Lagrangian multiplier network (ALaM) framework for stable learning of state-wise multipliers. ALaM consists of two key components. First, a quadratic penalty is introduced into the augmented Lagrangian to compensate for delayed multiplier updates and establish the local convexity near the optimum, thereby mitigating policy oscillations. Second, the multiplier network is trained via supervised regression toward a dual target, which stabilizes training and promotes convergence. Theoretically, we show that ALaM guarantees multiplier convergence and thus recovers the optimal policy of the constrained problem. Building on this framework, we integrate soft actor-critic (SAC) with ALaM to develop the SAC-ALaM algorithm. Experiments demonstrate that SAC-ALaM outperforms state-of-the-art safe RL baselines in both safety and return, while also stabilizing training dynamics and learning well-calibrated multipliers for risk identification.

Jiaming Zhang, Yujie Yang, Yao Lyu +2

Constrained RL Augmented Lagrangian Method Constrained Optimization Safe RL

Apr 30, 2026cs.LG

Global Optimality for Constrained Exploration via Penalty Regularization

Efficient exploration is a central problem in reinforcement learning and is often formalized as maximizing the entropy of the state-action occupancy measure. While unconstrained maximum-entropy exploration is relatively well understood, real-world exploration is often constrained by safety, resource, or imitation requirements. This constrained setting is particularly challenging because entropy maximization lacks additive structure, rendering Bellman-equation-based methods inapplicable. Moreover, scalable approaches require policy parameterization, inducing non-convexity in both the objective and the constraints. To our knowledge, the only prior model-free policy-gradient approach for this setting under general policy parameterization is due to Ying et al. (2025). Unfortunately, their guarantees are limited to weak regret and ergodic averages, which do not imply that the final output is a single deployable policy that is near-optimal and nearly feasible. In this work we take a different approach to this problem, and propose Policy Gradient Penalty (PGP) method, a single-loop policy-space method that enforces general convex occupancy-measure constraints via quadratic-penalty regularization. PGP constructs pseudo-rewards that yield gradient estimates of the penalized objective, subsequently exploiting the classical Policy Gradient Theorem. We further establish the regularity of the penalized objective, providing the smoothness properties needed to justify the convergence of PGP. Leveraging hidden convexity and strong duality, we then establish global last-iterate convergence guarantees, attaining an

ε

-optimal constrained entropy value with

ε

bounded constraint violation despite policy-induced non-convexity. We validate PGP through ablations on a grid-world benchmark and further demonstrate scalability on two challenging continuous-control tasks.

Florian Wolf, Ilyas Fatkhullin, Niao He

The Computing & Mathematical Sciences Department, California Institute of Technology, Pasadena, CA. · Department of Computer Science, ETH Zurich, Switzerland. · 3ETH AI Center, ETH Zurich, Switzerland.

Constrained RL Maximum Entropy RL Policy Gradient Methods Constrained Optimization

Apr 30, 2026cs.RO

Dynamic-TD3: A Novel Algorithm for UAV Path Planning with Dynamic Obstacle Trajectory Prediction

Deep reinforcement learning (DRL) finds extensive application in autonomous drone navigation within complex, high-risk environments. However, its practical deployment faces a safety-exploration dilemma: soft penalty mechanisms encourage risky trial-and-error, while most constraint-based methods suffer degraded performance under sensor noise and intent uncertainty. We propose Dynamic-TD3, a physically enhanced framework that enforces strict safety constraints while maintaining maneuverability by modeling navigation as a Constrained Markov Decision Process (CMDP). This framework integrates an Adaptive Trajectory Relational Evolution Mechanism (ATREM) to capture long-range intentions and employs a Physically Aware Gated Kalman Filter (PAG-KF) to mitigate non-stationary observation noise. The resulting state representation drives a dual-criterion policy that balances mission efficiency against hard safety constraints via Lagrangian relaxation. In experiments with aggressive dynamic threats, this approach demonstrates superior collision avoidance performance, reduced energy consumption, and smoother flight trajectories.

Wentao Chen, Jingtang Chen, Mingjian Fu +4

Reinforcement Learning UAV Navigation Constrained RL Dynamic Obstacle Avoidance Trajectory Prediction

Apr 29, 2026eess.SY

Learning to Route Electric Trucks Under Operational Uncertainty

Electric truck operations require routing decisions that remain feasible under limited battery range, long charging times, travel and energy consumption, and competition for shared charging infrastructure. These features make electric truck routing a coupled logistics and energy problem, limiting the practicality of heuristics-based methods and rendering them computationally infeasible at scale. This paper proposes a learning-based framework for the stochastic electric truck routing under charging constraints and operational uncertainty. The problem, solved by Reinforcement Learning, is formulated as an event-driven semi-Markov decision process with shared charging resources, stochastic travel and energy requirements, and realistic nonlinear fast-charging behavior. To support learning in this setting, a graph-based representation of system state and feasible decisions is introduced, together with a rule-based action mask that restricts policies to operationally admissible actions; thus, improving training efficiency. Building on this formulation, an event-driven simulation environment is developed that supports both Reinforcement Learning and benchmarking against heuristic and mathematical programming baselines. Computational experiments across a range of fleet sizes show that the proposed learning-based algorithm consistently outperforms baselines and attains performance close to optimization benchmarks in many settings, while preserving high success rates under charging congestion and uncertainty.

Stavros Orfanoudakis, Ziyan Li, Ruixiao Yang +4

Delft University of Technology, Intelligent Electrical Power Grids, Delft, The Netherlands · Massachusetts Institute of Technology, Center of Transportation and Logistics, Cambridge, MA, United States of America · Massachusetts Institute of Technology, Department of Aeronautics and Astronautics, Cambridge, MA, United States of America

Sequential Decision Making Electric Vehicle Charging Constrained RL Vehicle Routing