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We propose the concept of a Lagrangian game to solve constrained Markov games. Such games model scenarios where agents face cost constraints in addition to their individual rewards, that depend on both agent joint actions and the evolving…

Optimization and Control · Mathematics 2025-03-14 Soham Das , Santiago Paternain , Luiz F. O. Chamon , Ceyhun Eksin

Developing reinforcement learning algorithms that satisfy safety constraints is becoming increasingly important in real-world applications. In multi-agent reinforcement learning (MARL) settings, policy optimisation with safety awareness is…

Artificial Intelligence · Computer Science 2022-02-11 Shangding Gu , Jakub Grudzien Kuba , Munning Wen , Ruiqing Chen , Ziyan Wang , Zheng Tian , Jun Wang , Alois Knoll , Yaodong Yang

This paper considers offline multi-agent reinforcement learning. We propose the strategy-wise concentration principle which directly builds a confidence interval for the joint strategy, in contrast to the point-wise concentration principle…

Machine Learning · Computer Science 2022-10-17 Qiwen Cui , Simon S. Du

In this paper, we consider the problem of optimization and learning for constrained and multi-objective Markov decision processes, for both discounted rewards and expected average rewards. We formulate the problems as zero-sum games where…

Optimization and Control · Mathematics 2021-03-05 Ather Gattami , Qinbo Bai , Vaneet Agarwal

Multi-agent reinforcement learning (MARL) addresses sequential decision-making problems with multiple agents, where each agent optimizes its own objective. In many real-world instances, the agents may not only want to optimize their…

Machine Learning · Computer Science 2023-06-14 Pragnya Alatur , Giorgia Ramponi , Niao He , Andreas Krause

We study optimality for the safety-constrained Markov decision process which is the underlying framework for safe reinforcement learning. Specifically, we consider a constrained Markov decision process (with finite states and finite…

Systems and Control · Electrical Eng. & Systems 2023-07-13 Rahul Misra , Rafał Wisniewski , Carsten Skovmose Kallesøe

Constrained Markov games offer a formal mathematical framework for modeling multi-agent reinforcement learning problems where the behavior of the agents is subject to constraints. In this work, we focus on the recently introduced class of…

Machine Learning · Computer Science 2024-02-29 Philip Jordan , Anas Barakat , Niao He

In this paper, we study the learning of safe policies in the setting of reinforcement learning problems. This is, we aim to control a Markov Decision Process (MDP) of which we do not know the transition probabilities, but we have access to…

Systems and Control · Electrical Eng. & Systems 2022-01-14 Santiago Paternain , Miguel Calvo-Fullana , Luiz F. O. Chamon , Alejandro Ribeiro

This paper proposes a safe reinforcement learning (RL) algorithm that approximately solves the state-constrained optimal control problem for continuous-time uncertain nonlinear systems. We formulate the safe RL problem as the minimization…

Systems and Control · Electrical Eng. & Systems 2025-06-26 Soutrik Bandyopadhyay , Shubhendu Bhasin

Model-based algorithms -- algorithms that explore the environment through building and utilizing an estimated model -- are widely used in reinforcement learning practice and theoretically shown to achieve optimal sample efficiency for…

Machine Learning · Computer Science 2021-02-09 Qinghua Liu , Tiancheng Yu , Yu Bai , Chi Jin

During initial iterations of training in most Reinforcement Learning (RL) algorithms, agents perform a significant number of random exploratory steps. In the real world, this can limit the practicality of these algorithms as it can lead to…

Machine Learning · Computer Science 2022-10-17 Ashish Kumar Jayant , Shalabh Bhatnagar

This paper proposes a novel distributed approach for solving a cooperative Constrained Multi-agent Reinforcement Learning (CMARL) problem, where agents seek to minimize a global objective function subject to shared constraints. Unlike…

Systems and Control · Electrical Eng. & Systems 2026-05-08 Ali Kahe , Hamed Kebriaei

Constrained optimization is popularly seen in reinforcement learning for addressing complex control tasks. From the perspective of dynamic system, iteratively solving a constrained optimization problem can be framed as the temporal…

Machine Learning · Computer Science 2025-01-28 Tianqi Zhang , Puzhen Yuan , Guojian Zhan , Ziyu Lin , Yao Lyu , Zhenzhi Qin , Jingliang Duan , Liping Zhang , Shengbo Eben Li

We study offline multi-agent reinforcement learning (RL) in Markov games, where the goal is to learn an approximate equilibrium -- such as Nash equilibrium and (Coarse) Correlated Equilibrium -- from an offline dataset pre-collected from…

Machine Learning · Computer Science 2023-02-07 Yuheng Zhang , Yu Bai , Nan Jiang

We study online reinforcement learning in average-reward stochastic games (SGs). An SG models a two-player zero-sum game in a Markov environment, where state transitions and one-step payoffs are determined simultaneously by a learner and an…

Machine Learning · Computer Science 2017-12-05 Chen-Yu Wei , Yi-Te Hong , Chi-Jen Lu

Behavioral diversity, expert imitation, fairness, safety goals and others give rise to preferences in sequential decision making domains that do not decompose additively across time. We introduce the class of convex Markov games that allow…

Computer Science and Game Theory · Computer Science 2025-06-17 Ian Gemp , Andreas Haupt , Luke Marris , Siqi Liu , Georgios Piliouras

Lagrangian methods are widely used algorithms for constrained optimization problems, but their learning dynamics exhibit oscillations and overshoot which, when applied to safe reinforcement learning, leads to constraint-violating behavior…

Optimization and Control · Mathematics 2020-07-09 Adam Stooke , Joshua Achiam , Pieter Abbeel

In this paper, we present an online reinforcement learning algorithm for constrained Markov decision processes with a safety constraint. Despite the necessary attention of the scientific community, considering stochastic stopping time, the…

Machine Learning · Computer Science 2024-03-26 Abhijit Mazumdar , Rafal Wisniewski , Manuela L. Bujorianu

Markov Games (MG) is an important model for Multi-Agent Reinforcement Learning (MARL). It was long believed that the "curse of multi-agents" (i.e., the algorithmic performance drops exponentially with the number of agents) is unavoidable…

Machine Learning · Computer Science 2024-06-12 Yan Dai , Qiwen Cui , Simon S. Du

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…

Machine Learning · Computer Science 2026-04-02 Brenden Latham , Mehrdad Moharrami
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