Constrained RL

RL: Reinforcement Learning

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Overview

Constrained reinforcement learning studies how agents can maximize rewards while obeying limits on costs such as collisions, energy use, latency, or harm. Many methods model the problem as a constrained Markov decision process and use Lagrangian or primal-dual updates; others enforce feasibility with action masks, projections, safety shields, control barrier functions, or reachability analysis. These approaches are used in settings from robot control and power systems to language-model alignment, with work spanning online and offline learning, multi-agent tasks, and formal guarantees for regret and constraint satisfaction. A central challenge is balancing useful performance with reliable safety: average-cost limits can miss rare severe failures, while strict safeguards may make learning conservative or difficult to scale.

Latest papers

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226 papers38 papers in the last four weeks, up 46% on the four weeks before. 0.2% of all new papers.

May 4, 2026

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 PlanningDiffusion GuidanceConstrained RLOffline RLSafe RL
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May 4, 2026

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 LearningFederated RLExperience ReplayConstrained RLMulti-Agent Reinforcement Learning
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May 1, 2026

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

School of Vehicle and Mobility & College of AI, Tsinghua University, Beijing, 100084, China

Constrained RLAugmented Lagrangian MethodConstrained OptimizationSafe RL
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Apr 30, 2026

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 εε-optimal constrained entropy value with εε 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 RLMaximum Entropy RLPolicy Gradient MethodsConstrained Optimization
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Apr 30, 2026

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 LearningUAV NavigationConstrained RLDynamic Obstacle AvoidanceTrajectory Prediction
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Apr 29, 2026

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 MakingElectric Vehicle ChargingConstrained RLVehicle RoutingSemi-Markov Decision Process
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Apr 28, 2026

A Distributionally Robust Reinforcement Learning Framework for Constrained Urban EV Dispatch

We study city-scale control of electric-vehicle (EV) ride-hailing fleets where dispatch, repositioning, and charging decisions must respect charger and feeder limits under uncertain, spatially correlated demand and travel times. We formulate the problem as a hex-grid semi-Markov decision process (semi-MDP) with mixed actions -- discrete actions for serving, repositioning, and charging, together with continuous charging power -- and variable action durations. To guarantee physical feasibility during both training and deployment, the policy learns over high-level intentions produced by a masked, temperature-annealed actor. These intentions are projected at every decision step through a time-limited rolling mixed-integer linear program (MILP) that strictly enforces state-of-charge, port, and feeder constraints. To mitigate distributional shifts, we optimize a Soft Actor-Critic (SAC) agent against a Wasserstein-1 ambiguity set with a graph-aligned Mahalanobis ground metric that captures spatial correlations. The robust backup uses the Kantorovich-Rubinstein dual, a projected subgradient inner loop, and a primal-dual risk-budget update. Our architecture combines a two-layer Graph Convolutional Network (GCN) encoder, twin critics, and a value network that drives the adversary. Experiments on a large-scale EV fleet simulator built from NYC taxi data show that PD-RSAC achieves the highest net profit, reaching $1.22M, compared with $0.58M-$0.70M for strong heuristic, single-agent RL, and multi-agent RL baselines, including Greedy, SAC, MAPPO, and MADDPG, while maintaining zero feeder-limit violations.

An Nguyen, Hoang Nguyen, Phuong Le +3

College of Engineering and Computer Science, VinUniversity, Hanoi, Vietnam · Center for Environmental Intelligence, VinUniversity, Hanoi, Vietnam

Electric Vehicle ChargingConstrained RLDistributionally Robust OptimizationDistributionally Robust RLRobust RL
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Apr 27, 2026

GradMAP: Gradient-Based Multi-Agent Proximal Learning for Grid-Edge Flexibility

Coordinating large populations of grid-edge devices requires learning methods that remain fully decentralised in deployment while still respecting three-phase AC distribution-network physics. This paper proposes gradient-based multi-agent proximal learning (GradMAP) to address this challenge. GradMAP trains independent neural-network policies for each agent without any parameter sharing, and each agent uses only its own local observation for online decision-making without communication. During offline training, GradMAP embeds a differentiable three-phase AC power-flow model in a primal-dual learning loop and uses implicit differentiation to propagate exact network-constraint violations to update the policy parameters. To speed up training, GradMAP reuses expensive environment gradients through a proximal surrogate within a trust region defined in the more direct policy-output (action) space, instead of the probability distribution space used in other works, such as PPO. In case studies with 1,000 agents managing batteries, heat pumps, and controllable generators on the IEEE 123-bus feeder, GradMAP learns decentralised policies that minimise three-phase AC load-flow constraint violations within 15 minutes of training on a single workstation-class NVIDIA RTX PRO 5000 Blackwell 48GB GPU. This is a 3--5x training speed-up over gradient-based self-supervised learning benchmarks and substantially better training efficiency than multi-agent reinforcement-learning benchmarks. In out-of-sample tests, GradMAP also delivers among the lowest operating cost and constraint violations.

Yihong Zhou, Hongtai Zeng, Thomas Morstyn

Department of Engineering Science, University of Oxford

Multi-Agent ControlConstrained RLDecentralized MARLPower Systems
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Apr 26, 2026

CAPSULE: Control-Theoretic Action Perturbations for Safe Uncertainty-Aware Reinforcement Learning

Ensuring safe exploration in high-dimensional systems with unknown dynamics remains a significant challenge. Existing safe reinforcement learning methods often provide safety guarantees only in expectation, which can still lead to safety violations. Control-theoretic approaches, in contrast, offer hard constraint-based safety guarantees but typically assume access to known system dynamics or require accurate estimation of control-affine models. In this paper, we propose a safe reinforcement learning framework that learns a probabilistic control-affine dynamics model in an offline setting. The learned model is leveraged to explicitly construct control barrier functions (CBFs) that incorporate model uncertainty to provide conservative safety constraints. These CBF constraints are enforced through an online constraint-based action correction mechanism, enabling safe exploration without overly restricting task performance. Empirical evaluations on nonlinear, complex continuous-control benchmarks demonstrate that our approach achieves returns comparable to those of existing baselines while significantly reducing safety violations.

Rahul Narava, Siddharth Verma, Ojas Jain +2

Indian Institute of Technology Ropar · CRAN, Université de Lorraine

Control Barrier FunctionsConstrained RLSafe RLModel-Based RL
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Apr 25, 2026

Bridging Reasoning and Action: Hybrid LLM-RL Framework for Efficient Cross-Domain Task-Oriented Dialogue

Cross-domain task-oriented dialogue requires reasoning over implicit and explicit feasibility constraints while planning long-horizon, multi-turn actions. Large language models (LLMs) can infer such constraints but are unreliable over long horizons, while Reinforcement learning (RL) optimizes long-horizon behavior yet cannot recover constraints from raw dialogue. Naively coupling LLMs with RL is therefore brittle: unverified or unstructured LLM outputs can corrupt state representations and misguide policy learning. Motivated by this, we propose Verified LLM-Knowledge empowered RL (VLK-RL), a hybrid framework that makes LLM-derived constraint reasoning usable for RL. VLK-RL first elicits candidate constraints with an LLM and then verifies them via a dual-role cross-examination procedure to suppress hallucinations and cross-turn inconsistencies. The verified constraints are mapped into ontology-aligned slot-value representations, yielding a structured, constraint-aware state for RL policy optimization. Experiments across multiple benchmarks demonstrate that VLK-RL significantly improves generalization and robustness, outperforming strong single-model baselines on long-horizon tasks.

Yangyang Zhao, Linfan Dai, Li Cai +2

School of Computer Science and Technology, Changsha University of Science and Technology · School of Computer Science and Engineering, Central South University · Text Computing and Cognitive Intelligence MOE Engineering Research Center, Guizhou University +2

Constrained RLLLM-Guided RLConversational AgentsLong-Horizon LLM Agents
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Apr 24, 2026

Learning Control Policies to Provably Satisfy Hard Affine Constraints for Black-Box Hybrid Dynamical Systems

Ensuring safety for black-box hybrid dynamical systems presents significant challenges due to their instantaneous state jumps and unknown explicit nonlinear dynamics. Existing solutions for strict safety constraint satisfaction, like control barrier functions (CBFs) and reachability analysis, rely on direct knowledge of the dynamics. Similarly, safe reinforcement learning (RL) approaches often rely on known system dynamics or merely discourage safety violations through reward shaping. In this work, we want to learn RL policies which provably satisfy affine state constraints in closed loop for black-box hybrid dynamical systems with affine reset maps. Our key insight is forcing the RL policy to be affine and repulsive near the constraint boundaries for the unknown nonlinear dynamics of the system, providing guarantees that the trajectories will not violate the constraint. We further account for constraint violation due to instantaneous state jumps that occur due to impacts or reset maps in the hybrid system by introducing a second repulsive affine region before the reset that prevents post-reset states from violating the constraint. We derive sufficient conditions under which these policies satisfy safety constraints in closed loop. We also compare our approach with state-of-the-art reward shaping and learned-CBF methods on hybrid dynamical systems like the constrained pendulum and paddle juggler environments. In both scenarios, we show that our methodology learns higher quality policies while always satisfying the safety constraints.

Aayushi Shrivastava, Kartik Nagpal, Sairam Jinkala +2

Department of Mechanical Engineering, University of California Berkeley, Berkeley, CA 94709, USA

Dynamical SystemsSafety-Critical ControlConstrained RLSafe RL
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Apr 21, 2026

Policy Gradient Primal-Dual Method for Safe Reinforcement Learning from Human Feedback

Safe Reinforcement Learning from Human Feedback (Safe RLHF) has recently achieved empirical success in developing helpful and harmless large language models by decoupling human preferences regarding helpfulness and harmlessness. Existing approaches typically rely on fitting fixed horizon reward models from human feedback and have only been validated empirically. In this paper, we formulate safe RLHF as an infinite horizon discounted Con- strained Markov Decision Process (CMDP), since humans may interact with the model over a continuing sequence of interactions rather than within a single finite episode. We propose two Safe RLHF algorithms that do not require reward model fitting and, in contrast to prior work assuming fixed-length trajectories, support flexible trajectory lengths for training. Both algo- rithms are based on the primal-dual method and achieve global convergence guarantees with polynomial rates in terms of policy gradient iterations, trajectory sample lengths, and human preference queries. To the best of our knowledge, this is the first work to study infinite horizon discounted CMDP under human feedback and establish global, non-asymptotic convergence.

Qiang Liu, Adrienne Kline, Ermin Wei

Department of Electrical and Computer Engineering, Northwestern University, Evanston, IL, USA · Center for Artificial Intelligence, Bluhm Cardiovascular Institute, Northwestern Medicine, Chicago, IL, USA · Department of Surgery, Northwestern University, Chicago, IL, USA +3

Constrained RLPolicy Gradient MethodsConstrained OptimizationSafe RLRL from Human Feedback
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Apr 20, 2026

Physics-Informed Causal MDPs for Sequential Constraint Repair in Engineering Simulation Pipelines

Off-policy learning in constrained MDPs with large binary state spaces faces a fundamental tension: causal identification of transition dynamics requires structural assumptions, while sample-efficient policy learning requires state-space compression. We introduce PI-CMDP, a framework for CMDPs whose constraint dependencies form a layered DAG under a Lifecycle Ordering Assumption (LOA). We propose an Identify-Compress-Estimate pipeline: (i) Identify: LOA enables backdoor identification of causal edge weights for cross-layer pairs, with formal partial-identification bounds when LOA is violated; (ii) Compress: a Markov abstraction compresses state cardinality from 2^(WL) to (W+1)^L under layer-priority regularity and exchangeability; and (iii) Estimate: a physics-guided doubly-robust estimator remains unbiased and reduces the variance constant when the physics prior outperforms a learned model. We instantiate PI-CMDP on constraint repair in engineering simulation pipelines. On the TPS benchmark (4,206 episodes), PI-CMDP achieves 76.2% repair success rate with only 300 training episodes versus 70.8% for the strongest baseline (+5.4 pp), narrowing to +2.8 pp (83.4% vs. 80.6%) in the full-data regime, while substantially reducing cascade failure rates. All improvements are consistent across 5 independent seeds (paired t-test p < 0.02).

Chuhan Qiao

Beijing JiaoTong University

Markov Decision ProcessesReinforcement LearningConstrained RLCausal Inference
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Apr 15, 2026

Hierarchical Reinforcement Learning with Runtime Safety Shielding for Power Grid Operation

Reinforcement learning has shown promise for automating power-grid operation tasks such as topology control and congestion management. However, its deployment in real-world power systems remains limited by strict safety requirements, brittleness under rare disturbances, and poor generalization to unseen grid topologies. In safety-critical infrastructure, catastrophic failures cannot be tolerated, and learning-based controllers must operate within hard physical constraints. This paper proposes a safety-constrained hierarchical control framework for power-grid operation that explicitly decouples long-horizon decision-making from real-time feasibility enforcement. A high-level reinforcement learning policy proposes abstract control actions, while a deterministic runtime safety shield filters unsafe actions using fast forward simulation. Safety is enforced as a runtime invariant, independent of policy quality or training distribution. The proposed framework is evaluated on the Grid2Op benchmark suite under nominal conditions, forced line-outage stress tests, and zero-shot deployment on the ICAPS 2021 large-scale transmission grid without retraining. Results show that flat reinforcement learning policies are brittle under stress, while safety-only methods are overly conservative. In contrast, the proposed hierarchical and safety-aware approach achieves longer episode survival, lower peak line loading, and robust zero-shot generalization to unseen grids. These results indicate that safety and generalization in power-grid control are best achieved through architectural design rather than increasingly complex reward engineering, providing a practical path toward deployable learning-based controllers for real-world energy systems.

Gitesh Malik

Department of Electrical Engineering, Delhi Technological University (DTU), India

Safe RLPower SystemsHierarchical RLConstrained RLRuntime Assurance
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Apr 15, 2026

Optimistic Policy Learning under Pessimistic Adversaries with Regret and Violation Guarantees

Real-world decision-making systems operate in environments where state transitions depend not only on the agent's actions, but also on exogenous factors outside its control--competing agents, environmental disturbances, or strategic adversaries--formally, sh+1=f(sh,ah,aˉh)+ωhs_{h+1} = f(s_h, a_h, \bar{a}_h)+ω_h where aˉh\bar{a}_h is the adversary/external action, aha_h is the agent's action, and ωhω_h is an additive noise. Ignoring such factors can yield policies that are optimal in isolation but fail catastrophically in deployment, particularly when safety constraints must be satisfied. Standard Constrained MDP formulations assume the agent is the sole driver of state evolution, an assumption that breaks down in safety-critical settings. Existing robust RL approaches address this via distributional robustness over transition kernels, but do not explicitly model the strategic interaction between agent and exogenous factor, and rely on strong assumptions about divergence from a known nominal model. We model the exogenous factor as an adversarial policy πˉ\barπ that co-determines state transitions, and ask how an agent can remain both optimal and safe against such an adversary. To the best of our knowledge, this is the first work to study safety-constrained RL under explicit adversarial dynamics. We propose Robust Hallucinated Constrained Upper-Confidence RL (RHC-UCRL), a model-based algorithm that maintains optimism over both agent and adversary policies, explicitly separating epistemic from aleatoric uncertainty. RHC-UCRL achieves sub-linear regret and constraint violation guarantees.

Sourav Ganguly, Kartik Pandit, Arnob Ghosh

Dept. of Electrical and Computer Engineering, NJIT, Newark, NJ, USA

Adversarial MARLReinforcement LearningConstrained RLModel-Based RL
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Apr 14, 2026

Safe reinforcement learning with online filtering for fatigue-predictive human-robot task planning and allocation in production

Human-robot collaborative manufacturing, a core aspect of Industry 5.0, emphasizes ergonomics to enhance worker well-being. This paper addresses the dynamic human-robot task planning and allocation (HRTPA) problem, which involves determining when to perform tasks and who should execute them to maximize efficiency while ensuring workers' physical fatigue remains within safe limits. The inclusion of fatigue constraints, combined with production dynamics, significantly increases the complexity of the HRTPA problem. Traditional fatigue-recovery models in HRTPA often rely on static, predefined hyperparameters. However, in practice, human fatigue sensitivity varies daily due to factors such as changed work conditions and insufficient sleep. To better capture this uncertainty, we treat fatigue-related parameters as inaccurate and estimate them online based on observed fatigue progression during production. To address these challenges, we propose PF-CD3Q, a safe reinforcement learning (safe RL) approach that integrates the particle filter with constrained dueling double deep Q-learning for real-time fatigue-predictive HRTPA. Specifically, we first develop PF-based estimators to track human fatigue and update fatigue model parameters in real-time. These estimators are then integrated into CD3Q by making task-level fatigue predictions during decision-making and excluding tasks that exceed fatigue limits, thereby constraining the action space and formulating the problem as a constrained Markov decision process (CMDP).

Jintao Xue, Xiao Li, Nianmin Zhang

CI3 Lab, Department of Civil Engineering, The University of Hong Kong, Hong Kong SAR

Human-Robot CollaborationSafe RLConstrained RL
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Apr 13, 2026

Load constrained wind farm flow control through multi-objective multi-agent reinforcement learning

This study presents a multi-agent reinforcement learning (MARL) framework for load-constrained wind farm flow control (WFFC). While wake steering can enhance total wind farm power, it often introduces increased structural loads on downstream turbines. To address this, we integrate an Independent Soft Actor-Critic (I-SAC) architecture with a data-driven, local inflow sector-averaged surrogate model to provide real-time estimates of Damage Equivalent Loads (DELs). By incorporating these estimates into a shaped reward function, turbine-specific agents are trained to maximize power production while adhering to specific load-increase thresholds (ΔmaxΔ_{max}) of 10%, 20%, and 30% relative to a baseline controller. The framework is implemented within the WindGym environment using the DYNAMIKS flow solver with Dynamic Wake Meandering (DWM) model to capture non-stationary wake physics. Results indicate that the MARL agents successfully learn collaborative policies that prioritise power gain while actively retreating from high-DEL control strategies.

Teodor Åstrand, Marcus Binder Nilsen, Iasonas Tsaklis +3

Department of Wind and Energy Systems, Technical University of Denmark, Roskilde, Denmark

Multi-Agent Reinforcement LearningConstrained RLMulti-Objective Reinforcement Learning
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Apr 11, 2026

A Dual-Positive Monotone Parameterization for Multi-Segment Bids and a Validity Assessment Framework for Reinforcement Learning Agent-based Simulation of Electricity Markets

Reinforcement learning agent-based simulation (RL-ABS) has become an important tool for electricity market mechanism analysis and evaluation. In the modeling of monotone, bounded, multi-segment stepwise bids, existing methods typically let the policy network first output an unconstrained action and then convert it into a feasible bid curve satisfying monotonicity and boundedness through post-processing mappings such as sorting, clipping, or projection. However, such post-processing mappings often fail to satisfy continuous differentiability, injectivity, and invertibility at boundaries or kinks, thereby causing gradient distortion and leading to spurious convergence in simulation results. Meanwhile, most existing studies conduct mechanism analysis and evaluation mainly on the basis of training-curve convergence, without rigorously assessing the distance between the simulation outcomes and Nash equilibrium, which severely undermines the credibility of the results. To address these issues, this paper proposes...

Zunnan Xu, Zhaoxia Jing, Zhanhua Pan

School of Electric Power Engineering, South China University of Technology, Guangzhou, 510640, Guangdong, China · Department of Engineering, University of Exeter, Exeter EX4 4PY, U.K.

Automated BiddingConstrained RLAgent-Based ModelingMulti-Agent Reinforcement Learning
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Apr 9, 2026

Faithful GRPO: Improving Visual Spatial Reasoning in Multimodal Language Models via Constrained Policy Optimization

Multimodal reasoning models (MRMs) trained with reinforcement learning with verifiable rewards (RLVR) show improved accuracy on visual reasoning benchmarks. However, we observe that accuracy gains often come at the cost of reasoning quality: generated Chain-of-Thought (CoT) traces are frequently inconsistent with the final answer and poorly grounded in the visual evidence. We systematically study this phenomenon across seven challenging real-world spatial reasoning benchmarks and find that it affects contemporary MRMs such as ViGoRL-Spatial, TreeVGR as well as our own models trained with standard Group Relative Policy Optimization (GRPO). We characterize CoT reasoning quality along two complementary axes: "logical consistency" (does the CoT entail the final answer?) and "visual grounding" (does each reasoning step accurately describe objects, attributes, and spatial relationships in the image?). To address this, we propose Faithful GRPO (FGRPO), a variant of GRPO that enforces consistency and grounding as constraints via Lagrangian dual ascent. FGRPO incorporates batch-level consistency and grounding constraints into the advantage computation within a group, adaptively adjusting the relative importance of constraints during optimization. We evaluate FGRPO on Qwen2.5-VL-7B and 3B backbones across seven spatial datasets. Our results show that FGRPO substantially improves reasoning quality, reducing the inconsistency rate from 24.5% to 1.7% and improving visual grounding scores by +13%. It also improves final answer accuracy over simple GRPO, demonstrating that faithful reasoning enables better answers.

Sai Srinivas Kancheti, Aditya Kanade, Rohit Sinha +2

CSE Dept., IIT Hyderabad, Hyderabad, India · Microsoft Research, Bengaluru, India

Visual Spatial ReasoningMultimodal CoT ReasoningFaithfulness in VLMsRL for VLMsConstrained RLMultimodal Grounding
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Apr 8, 2026

Reinforcement Learning with Reward Machines for Sleep Control in Mobile Networks

Energy efficiency in mobile networks is crucial for sustainable telecommunications infrastructure, particularly as network densification continues to increase power consumption. Sleep mechanisms for the components in mobile networks can reduce energy use, but deciding which components to put to sleep, when, and for how long while preserving quality of service (QoS) remains a difficult optimisation problem. In this paper, we utilise reinforcement learning with reward machines (RMs) to make sleep-control decisions that balance immediate energy savings and long-term QoS impact, i.e. time-averaged packet drop rates for deadline-constrained traffic and time-averaged minimum-throughput guarantees for constant-rate users. A challenge is that time-averaged constraints depend on cumulative performance over time rather than immediate performance. As a result, the effective reward is non-Markovian, and optimal actions depend on operational history rather than the instantaneous system state. RMs account for the history dependence by maintaining an abstract state that explicitly tracks the QoS constraint violations over time. Our framework provides a principled, scalable approach to energy management for next-generation mobile networks under diverse traffic patterns and QoS requirements.

Kristina Levina, Nikolaos Pappas, Athanasios Karapantelakis +2

Department of Computer and Information Science, Linköping University, Linköping, Sweden · Ericsson Research

Wireless CommunicationsReinforcement LearningConstrained RL
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Apr 6, 2026

Boosted Distributional Reinforcement Learning: Analysis and Healthcare Applications

Researchers and practitioners are increasingly considering reinforcement learning to optimize decisions in complex domains like robotics and healthcare. To date, these efforts have largely utilized expectation-based learning. However, relying on expectation-focused objectives may be insufficient for making consistent decisions in highly uncertain situations involving multiple heterogeneous groups. While distributional reinforcement learning algorithms have been introduced to model the full distributions of outcomes, they can yield large discrepancies in realized benefits among comparable agents. This challenge is particularly acute in healthcare settings, where physicians (controllers) must manage multiple patients (subordinate agents) with uncertain disease progression and heterogeneous treatment responses. We propose a Boosted Distributional Reinforcement Learning (BDRL) algorithm that optimizes agent-specific outcome distributions while enforcing comparability among similar agents and analyze its convergence. To further stabilize learning, we incorporate a post-update projection step formulated as a constrained convex optimization problem, which efficiently aligns individual outcomes with a high-performing reference within a specified tolerance. We apply our algorithm to manage hypertension in a large subset of the US adult population by categorizing individuals into cardiovascular disease risk groups. Our approach modifies treatment plans for median and vulnerable patients by mimicking the behavior of high-performing references in each risk group. Furthermore, we find that BDRL improves the number and consistency of quality-adjusted life years compared with reinforcement learning baselines.

Zequn Chen, Wesley J. Marrero

Thayer School of Engineering, Dartmouth College

Reinforcement LearningDistributional RLConstrained RL
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Apr 5, 2026

MC-CPO: Mastery-Conditioned Constrained Policy Optimization for Pedagogically Safe Intelligent Tutoring Systems

Intelligent tutoring systems increasingly rely on reinforcement learning to personalise instruction, yet optimising for observable engagement signals can systematically decouple learner activity from genuine knowledge acquisition. Analysing over 21 million student interactions across two deployed platforms, we find engagement events without corresponding mastery gains occur in 26.5% of interactions on Junyi Academy (72,758 students) and 3.1% on XES3G5M (14,453 students, NeurIPS 2023), confirming this pattern is directly observable in deployed educational technology at scale. We introduce Mastery-Conditioned Constrained Policy Optimisation (MC-CPO), a reinforcement learning framework that addresses this problem structurally. MC-CPO conditions the admissible instructional action space on learner mastery state: a concept becomes available only when prerequisite knowledge meets a mastery threshold, yielding an action space that expands naturally as learners acquire knowledge. Pedagogical safety constraints are enforced by construction, with formal guarantees of structural prerequisite safety, primal-dual convergence, and strict dominance over post-hoc filtering. MC-CPO is the only method to reduce reward hacking severity across all conditions. Mean per-episode mastery gain increases by 18.3% on Junyi Academy and 54.0% on XES3G5M relative to all baselines, while competitive engagement performance is maintained. These results support structural constraint modelling as a principled foundation for safer adaptive instructional policies in deployed tutoring systems.

Oluseyi Olukola, Nick Rahimi

School of Computing Sciences and Computer Engineering University of Southern Mississippi Hattiesburg MS 39406 USA

Intelligent Tutoring SystemsPolicy LearningSafe RLConstrained RLReward Hacking
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Apr 3, 2026

Improving Feasibility via Fast Autoencoder-Based Projections

Enforcing complex (e.g., nonconvex) operational constraints is a critical challenge in real-world learning and control systems. However, existing methods struggle to efficiently enforce general classes of constraints. To address this, we propose a novel data-driven amortized approach that uses a trained autoencoder as an approximate projector to provide fast corrections to infeasible predictions. Specifically, we train an autoencoder using an adversarial objective to learn a structured, convex latent representation of the feasible set. This enables rapid correction of neural network outputs by projecting their associated latent representations onto a simple convex shape before decoding into the original feasible set. We test our approach on a diverse suite of constrained optimization and reinforcement learning problems with challenging nonconvex constraints. Results show that our method effectively enforces constraints at a low computational cost, offering a practical alternative to expensive feasibility correction techniques based on traditional solvers.

Maria Chzhen, Priya L. Donti

University of Toronto Toronto, ON, Canada · Massachusetts Institute of Technology Cambridge, MA, USA

Constrained OptimizationConstrained RLAutoencoders
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Apr 3, 2026

Behavior-Constrained Reinforcement Learning with Receding-Horizon Credit Assignment for High-Performance Control

Learning high-performance control policies that remain consistent with expert behavior is a fundamental challenge in robotics. Reinforcement learning can discover high-performing strategies but often departs from desirable human behavior, whereas imitation learning is limited by demonstration quality and struggles to improve beyond expert data. We propose a behavior-constrained reinforcement learning framework that improves beyond demonstrations while explicitly controlling deviation from expert behavior. Because expert-consistent behavior in dynamic control is inherently trajectory-level, we introduce a receding-horizon predictive mechanism that models short-term future trajectories and provides look-ahead rewards during training. To account for the natural variability of human behavior under disturbances and changing conditions, we further condition the policy on reference trajectories, allowing it to represent a distribution of expert-consistent behaviors rather than a single deterministic target. Empirically, we evaluate the approach in high-fidelity race car simulation using data from professional drivers, a domain characterized by extreme dynamics and narrow performance margins. The learned policies achieve competitive lap times while maintaining close alignment with expert driving behavior, outperforming baseline methods in both performance and imitation quality. Beyond standard benchmarks, we conduct human-grounded evaluation in a driver-in-the-loop simulator and show that the learned policies reproduce setup-dependent driving characteristics consistent with the feedback of top-class professional race drivers. These results demonstrate that our method enables learning high-performance control policies that are both optimal and behavior-consistent, and can serve as reliable surrogates for human decision-making in complex control systems.

Siwei Ju, Jan Tauberschmidt, Oleg Arenz +2

Intelligent Autonomous Systems Lab, Department of Computer Science, TU Darmstadt, Germany. · Porsche AG, Stuttgart, Germany. · German Research Center for Artificial Intelligence (DFKI), Germany.

Constrained RLRL for Autonomous DrivingCredit Assignment in RLImitation Learning
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Apr 1, 2026

Tool-Augmented Agent for Closed-loop Optimization,Simulation,and Modeling Orchestration

Iterative industrial design-simulation optimization is bottlenecked by the CAD-CAE semantic gap: translating simulation feedback into valid geometric edits under diverse, coupled constraints. To fill this gap, we propose COSMO-Agent (Closed-loop Optimization, Simulation, and Modeling Orchestration), a tool-augmented reinforcement learning (RL) framework that teaches LLMs to complete the closed-loop CAD-CAE process. Specifically, we cast CAD generation, CAE solving, result parsing, and geometry revision as an interactive RL environment, where an LLM learns to orchestrate external tools and revise parametric geometries until constraints are satisfied. To make this learning stable and industrially usable, we design a multi-constraint reward that jointly encourages feasibility, toolchain robustness, and structured output validity. In addition, we contribute an industry-aligned dataset that covers 25 component categories with executable CAD-CAE tasks to support realistic training and evaluation. Experiments show that COSMO-Agent training substantially improves small open-source LLMs for constraint-driven design, exceeding large open-source and strong closed-source models in feasibility, efficiency, and stability.

Liyuan Deng, Shujian Deng, Yongkang Chen +6

Northwestern Polytechnical University · Shanghai Artificial Intelligence Laboratory

LLM Agent OrchestrationConstrained OptimizationRL for Tool UseParametric CAD ModelingConstrained RL
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Mar 31, 2026

Autonomous Adaptive Solver Selection for Chemistry Integration via Reinforcement Learning

The computational cost of stiff chemical kinetics remains a dominant bottleneck in reacting-flow simulation, yet hybrid integration strategies are typically driven by hand-tuned heuristics or supervised predictors that make myopic decisions from instantaneous local state. We introduce a constrained reinforcement learning (RL) framework that autonomously selects between an implicit BDF integrator (CVODE) and a quasi-steady-state (QSS) solver during chemistry integration. Solver selection is cast as a Markov decision process. The agent learns trajectory-aware policies that account for how present solver choices influence downstream error accumulation, while minimizing computational cost under a user-prescribed accuracy tolerance enforced through a Lagrangian reward with online multiplier adaptation. Across sampled 0D homogeneous reactor conditions, the RL-adaptive policy achieves a mean speedup of approximately 3×3\times, with speedups ranging from 1.11×1.11\times to 10.58×10.58\times, while maintaining accurate ignition delays and species profiles for a 106-species n-dodecane mechanism and adding approximately 1%1\% inference overhead. Without retraining, the 0D-trained policy transfers to 1D counterflow diffusion flames over strain rates 1010--2000 s−12000~\mathrm{s}^{-1}, delivering consistent ≈2.2×\approx 2.2\times speedup relative to CVODE while preserving near-reference temperature accuracy and selecting CVODE at only 1212--15%15\% of space-time points. Overall, the results demonstrate the potential of the proposed reinforcement learning framework to learn problem-specific integration strategies while respecting accuracy constraints, thereby opening a pathway toward adaptive, self-optimizing workflows for multiphysics systems with spatially heterogeneous stiffness.

Eloghosa Ikponmwoba, Opeoluwa Owoyele

Department of Mechanical and Industrial Engineering Louisiana State University Baton Rouge, LA 70803

Reinforcement LearningConstrained RLComputational Fluid Dynamics
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Mar 31, 2026

Offline Constrained RLHF with Multiple Preference Oracles

We study offline constrained reinforcement learning from human feedback with multiple preference oracles. Motivated by applications that trade off performance with safety or fairness, we aim to maximize target population utility subject to a minimum protected group welfare constraint. From pairwise comparisons collected under a reference policy, we estimate oracle-specific rewards via maximum likelihood and analyze how statistical uncertainty propagates through the dual program. We cast the constrained objective as a KL-regularized Lagrangian whose primal optimizer is a Gibbs policy, reducing learning to a convex dual problem. We propose a dual-only algorithm that ensures high-probability constraint satisfaction and provide the first finite-sample performance guarantees for offline constrained preference learning. Finally, we extend our theoretical analysis to accommodate multiple constraints and general f-divergence regularization.

Brenden Latham, Mehrdad Moharrami

Computer Science Department, University of Iowa, Iowa City, IA, USA

Constrained RLReinforcement LearningRL from Human FeedbackPreference-Based RLOffline RL
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Mar 29, 2026

Near-Optimal Primal-Dual Algorithm for Learning Linear Mixture CMDPs with Adversarial Rewards

We study safe reinforcement learning in finite-horizon linear mixture constrained Markov decision processes (CMDPs) with adversarial rewards under full-information feedback and an unknown transition kernel. We propose a primal-dual policy optimization algorithm that achieves regret and constraint violation bounds of O~(d2H3K)\widetilde{O}(\sqrt{d^2 H^3 K}) under mild conditions, where dd is the feature dimension, HH is the horizon, and KK is the number of episodes. To the best of our knowledge, this is the first provably efficient algorithm for linear mixture CMDPs with adversarial rewards. In particular, our regret bound is near-optimal, matching the known minimax lower bound up to logarithmic factors. The key idea is to introduce a regularized dual update that enables a drift-based analysis. This step is essential, as strong duality-based analysis cannot be directly applied when reward functions change across episodes. In addition, we extend weighted ridge regression-based parameter estimation to the constrained setting, allowing us to construct tighter confidence intervals that are crucial for deriving the near-optimal regret bound.

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 +2

Adversarial MARLReinforcement LearningConstrained RLMarkov Decision ProcessesRegret Minimization in RL
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Mar 28, 2026

Dynamic resource matching in manufacturing using deep reinforcement learning

Matching plays an important role in the logical allocation of resources across a wide range of industries. The benefits of matching have been increasingly recognized in manufacturing industries. In particular, capacity sharing has received much attention recently. In this paper, we consider the problem of dynamically matching demand-capacity types of manufacturing resources. We formulate the multi-period, many-to-many manufacturing resource-matching problem as a sequential decision process. The formulated manufacturing resource-matching problem involves large state and action spaces, and it is not practical to accurately model the joint distribution of various types of demands. To address the curse of dimensionality and the difficulty of explicitly modeling the transition dynamics, we use a model-free deep reinforcement learning approach to find optimal matching policies. Moreover, to tackle the issue of infeasible actions and slow convergence due to initial biased estimates caused by the maximum operator in Q-learning, we introduce two penalties to the traditional Q-learning algorithm: a domain knowledge-based penalty based on a prior policy and an infeasibility penalty that conforms to the demand-supply constraints. We establish theoretical results on the convergence of our domain knowledge-informed Q-learning providing performance guarantee for small-size problems. For large-size problems, we further inject our modified approach into the deep deterministic policy gradient (DDPG) algorithm, which we refer to as domain knowledge-informed DDPG (DKDDPG). In our computational study, including small- and large-scale experiments, DKDDPG consistently outperformed traditional DDPG and other RL algorithms, yielding higher rewards and demonstrating greater efficiency in time and episodes.

Saunak Kumar Panda, Yisha Xiang, Ruiqi Liu

Department of Industrial Engineering, University of Houston, Houston, TX 77004, USA · Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 79409, USA

ManufacturingRL for Combinatorial OptimizationModel-Free RLDeep Deterministic Policy GradientConstrained RL
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Mar 25, 2026

Off-Policy Safe Reinforcement Learning with Constrained Optimistic Exploration

When safety is formulated as a limit of cumulative cost, safe reinforcement learning (RL) aims to learn policies that maximize return subject to the cost constraint in data collection and deployment. Off-policy safe RL methods, although offering high sample efficiency, suffer from constraint violations due to cost-agnostic exploration and estimation bias in cumulative cost. To address this issue, we propose Constrained Optimistic eXploration Q-learning (COX-Q), an off-policy safe RL algorithm that integrates cost-bounded online exploration and conservative offline distributional value learning. First, we introduce a novel cost-constrained optimistic exploration strategy that resolves gradient conflicts between reward and cost in the action space and adaptively adjusts the trust region to control the training cost. Second, we adopt truncated quantile critics to stabilize the cost value learning. Quantile critics also quantify epistemic uncertainty to guide exploration. Experiments on safe velocity, safe navigation, and autonomous driving tasks demonstrate that COX-Q achieves high sample efficiency, competitive test safety performance, and controlled data collection cost. The results highlight COX-Q as a promising RL method for safety-critical applications.

Guopeng Li, Matthijs T. J. Spaan, Julian F. P. Kooij

Faculty of Electrical Engineering, Mathematics and Computer Science, Delft University of Technology, Delft, the Netherlands

Safe RLConstrained RLOff-Policy RLRL Exploration
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