Local Optimization Achieves Global Optimality in Multi-Agent Reinforcement Learning

TL;DR

This paper introduces a provably convergent multi-agent PPO algorithm that leverages local optimization to achieve global optimality in cooperative Markov games, supported by theoretical guarantees and experimental validation.

Contribution

It presents the first provably convergent multi-agent PPO algorithm with theoretical guarantees and extends it to off-policy settings with pessimism for improved performance.

Findings

Algorithm converges to global optimum at a sublinear rate

Extension to off-policy setting with pessimism improves evaluation

First provably convergent multi-agent PPO in cooperative games

Abstract

Policy optimization methods with function approximation are widely used in multi-agent reinforcement learning. However, it remains elusive how to design such algorithms with statistical guarantees. Leveraging a multi-agent performance difference lemma that characterizes the landscape of multi-agent policy optimization, we find that the localized action value function serves as an ideal descent direction for each local policy. Motivated by the observation, we present a multi-agent PPO algorithm in which the local policy of each agent is updated similarly to vanilla PPO. We prove that with standard regularity conditions on the Markov game and problem-dependent quantities, our algorithm converges to the globally optimal policy at a sublinear rate. We extend our algorithm to the off-policy setting and introduce pessimism to policy evaluation, which aligns with experiments. To our knowledge, this is the first provably convergent multi-agent PPO algorithm in cooperative Markov games.