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

TL;DR

This paper introduces a game-theoretic framework for multi-objective reinforcement learning using max-min criteria, providing a convergent algorithm with theoretical guarantees and superior empirical performance.

Contribution

It reformulates max-min MORL as a zero-sum game and develops an efficient mirror descent algorithm with convergence proofs and adaptive regularization.

Findings

Algorithm converges in tabular settings

Deep RL implementation outperforms baselines

Provides theoretical iteration and sample complexity bounds

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.