Convex Markov Games: A New Frontier for Multi-Agent Reinforcement Learning

TL;DR

This paper introduces convex Markov games, a broad class of multi-agent decision models that accommodate complex preferences and guarantees the existence of equilibria, enabling new solutions for fairness, safety, and strategic behavior in multi-agent systems.

Contribution

It defines convex Markov games with general convex preferences, proves the existence of pure strategy Nash equilibria, and develops empirical methods to approximate these equilibria.

Findings

Successfully solved classic repeated normal-form games.

Found fair solutions in asymmetric coordination scenarios.

Achieved safe, long-term behaviors in a robot warehouse environment.

Abstract

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 general convex preferences over occupancy measures. Despite infinite time horizon and strictly higher generality than Markov games, pure strategy Nash equilibria exist. Furthermore, equilibria can be approximated empirically by performing gradient descent on an upper bound of exploitability. Our experiments reveal novel solutions to classic repeated normal-form games, find fair solutions in a repeated asymmetric coordination game, and prioritize safe long-term behavior in a robot warehouse environment. In the prisoner's dilemma, our algorithm leverages transient imitation to find a policy profile that deviates from observed human play only slightly, yet achieves higher per-player utility while also being three orders of magnitude less exploitable.