Convergence of Decentralized Actor-Critic Algorithm in General-sum Markov Games

TL;DR

This paper analyzes the convergence of a decentralized actor-critic algorithm in general-sum Markov games, introducing the Markov Near-Potential Function to characterize strategy convergence without requiring full knowledge of other agents.

Contribution

It extends convergence analysis to general-sum Markov games using a decentralized actor-critic method with an innovative Lyapunov function, the MNPF.

Findings

Demonstrates convergence properties of decentralized learning in general-sum Markov games.

Introduces the Markov Near-Potential Function as an approximate Lyapunov function.

Provides conditions under which the algorithm converges to Nash equilibria.

Abstract

Markov games provide a powerful framework for modeling strategic multi-agent interactions in dynamic environments. Traditionally, convergence properties of decentralized learning algorithms in these settings have been established only for special cases, such as Markov zero-sum and potential games, which do not fully capture real-world interactions. In this paper, we address this gap by studying the asymptotic properties of learning algorithms in general-sum Markov games. In particular, we focus on a decentralized algorithm where each agent adopts an actor-critic learning dynamic with asynchronous step sizes. This decentralized approach enables agents to operate independently, without requiring knowledge of others' strategies or payoffs. We introduce the concept of a Markov Near-Potential Function (MNPF) and demonstrate that it serves as an approximate Lyapunov function for the policy updates in the decentralized learning dynamics, which allows us to characterize the convergent set of strategies. We further strengthen our result under specific regularity conditions and with finite Nash equilibria.