Breaking the Curse of Multiagency in Robust Multi-Agent Reinforcement Learning

TL;DR

This paper introduces a novel class of distributionally robust Markov games inspired by behavioral economics, providing a sample-efficient algorithm that overcomes the exponential complexity typically associated with multiple agents in robust multi-agent reinforcement learning.

Contribution

It formulates a new class of RMGs considering agents' behaviors, proves the existence of solutions, and develops the first polynomial-sample complexity algorithm to break the curse of multiagency.

Findings

Established well-posedness of the new RMG class.

Proposed a polynomial-sample complexity algorithm for CCE.

First to overcome the curse of multiagency in RMGs.

Abstract

Standard multi-agent reinforcement learning (MARL) algorithms are vulnerable to sim-to-real gaps. To address this, distributionally robust Markov games (RMGs) have been proposed to enhance robustness in MARL by optimizing the worst-case performance when game dynamics shift within a prescribed uncertainty set. RMGs remains under-explored, from reasonable problem formulation to the development of sample-efficient algorithms. Two notorious and open challenges are the formulation of the uncertainty set and whether the corresponding RMGs can overcome the curse of multiagency, where the sample complexity scales exponentially with the number of agents. In this work, we propose a natural class of RMGs inspired by behavioral economics, where each agent's uncertainty set is shaped by both the environment and the integrated behavior of other agents. We first establish the well-posedness of this class of RMGs by proving the existence of game-theoretic solutions such as robust Nash equilibria and coarse correlated equilibria (CCE). Assuming access to a generative model, we then introduce a sample-efficient algorithm for learning the CCE whose sample complexity scales polynomially with all relevant parameters. To the best of our knowledge, this is the first algorithm to break the curse of multiagency for RMGs, regardless of the uncertainty set formulation.