Multi-Objective Reinforcement Learning with Max-Min Criterion: A Game-Theoretic Approach

• URL: http://arxiv.org/abs/2510.20235v1
• Date: Thu, 23 Oct 2025 05:39:26 GMT
• Title: Multi-Objective Reinforcement Learning with Max-Min Criterion: A Game-Theoretic Approach
• Authors: Woohyeon Byeon, Giseung Park, Jongseong Chae, Amir Leshem, Youngchul Sung,
• Abstract summary: We reformulate max-min multi-objective reinforcement learning as a two-player zero-sum regularized continuous game.<n>Our approach simplifies the policy update while ensuring global last-iterate convergence.<n>Our implementation for deep reinforcement learning significantly outperforms previous baselines in many MORL environments.
• Score: 25.475842473998906
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: In this paper, we propose a provably convergent and practical framework for multi-objective reinforcement learning with max-min criterion. From a game-theoretic perspective, we reformulate max-min multi-objective reinforcement learning as a two-player zero-sum regularized continuous game and introduce an efficient algorithm based on mirror descent. Our approach simplifies the policy update while ensuring global last-iterate convergence. We provide a comprehensive theoretical analysis on our algorithm, including iteration complexity under both exact and approximate policy evaluations, as well as sample complexity bounds. To further enhance performance, we modify the proposed algorithm with adaptive regularization. Our experiments demonstrate the convergence behavior of the proposed algorithm in tabular settings, and our implementation for deep reinforcement learning significantly outperforms previous baselines in many MORL environments.

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