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.
@article{arxiv.2305.04819,
title = {Local Optimization Achieves Global Optimality in Multi-Agent Reinforcement Learning},
author = {Yulai Zhao and Zhuoran Yang and Zhaoran Wang and Jason D. Lee},
journal= {arXiv preprint arXiv:2305.04819},
year = {2023}
}