Local Optimization Achieves Global Optimality in Multi-Agent Reinforcement Learning

Yulai Zhao, Zhuoran Yang, Zhaoran Wang, Jason D. Lee
Proceedings of the 40th International Conference on Machine Learning, PMLR 202:42200-42226, 2023.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v202-zhao23j, title = {Local Optimization Achieves Global Optimality in Multi-Agent Reinforcement Learning}, author = {Zhao, Yulai and Yang, Zhuoran and Wang, Zhaoran and Lee, Jason D.}, booktitle = {Proceedings of the 40th International Conference on Machine Learning}, pages = {42200--42226}, year = {2023}, editor = {Krause, Andreas and Brunskill, Emma and Cho, Kyunghyun and Engelhardt, Barbara and Sabato, Sivan and Scarlett, Jonathan}, volume = {202}, series = {Proceedings of Machine Learning Research}, month = {23--29 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v202/zhao23j/zhao23j.pdf}, url = {https://proceedings.mlr.press/v202/zhao23j.html}, 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.} }
Endnote
%0 Conference Paper %T Local Optimization Achieves Global Optimality in Multi-Agent Reinforcement Learning %A Yulai Zhao %A Zhuoran Yang %A Zhaoran Wang %A Jason D. Lee %B Proceedings of the 40th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2023 %E Andreas Krause %E Emma Brunskill %E Kyunghyun Cho %E Barbara Engelhardt %E Sivan Sabato %E Jonathan Scarlett %F pmlr-v202-zhao23j %I PMLR %P 42200--42226 %U https://proceedings.mlr.press/v202/zhao23j.html %V 202 %X 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.
APA
Zhao, Y., Yang, Z., Wang, Z. & Lee, J.D.. (2023). Local Optimization Achieves Global Optimality in Multi-Agent Reinforcement Learning. Proceedings of the 40th International Conference on Machine Learning, in Proceedings of Machine Learning Research 202:42200-42226 Available from https://proceedings.mlr.press/v202/zhao23j.html.

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