Offline Learning in Markov Games with General Function Approximation

Yuheng Zhang, Yu Bai, Nan Jiang
Proceedings of the 40th International Conference on Machine Learning, PMLR 202:40804-40829, 2023.

Abstract

We study offline multi-agent reinforcement learning (RL) in Markov games, where the goal is to learn an approximate equilibrium—such as Nash equilibrium and (Coarse) Correlated Equilibrium—from an offline dataset pre-collected from the game. Existing works consider relatively restricted tabular or linear models and handle each equilibria separately. In this work, we provide the first framework for sample-efficient offline learning in Markov games under general function approximation, handling all 3 equilibria in a unified manner. By using Bellman-consistent pessimism, we obtain interval estimation for policies’ returns, and use both the upper and the lower bounds to obtain a relaxation on the gap of a candidate policy, which becomes our optimization objective. Our results generalize prior works and provide several additional insights. Importantly, we require a data coverage condition that improves over the recently proposed “unilateral concentrability”. Our condition allows selective coverage of deviation policies that optimally trade-off between their greediness (as approximate best responses) and coverage, and we show scenarios where this leads to significantly better guarantees. As a new connection, we also show how our algorithmic framework can subsume seemingly different solution concepts designed for the special case of two-player zero-sum games.

Cite this Paper

BibTeX
@InProceedings{pmlr-v202-zhang23a, title = {Offline Learning in {M}arkov Games with General Function Approximation}, author = {Zhang, Yuheng and Bai, Yu and Jiang, Nan}, booktitle = {Proceedings of the 40th International Conference on Machine Learning}, pages = {40804--40829}, 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/zhang23a/zhang23a.pdf}, url = {https://proceedings.mlr.press/v202/zhang23a.html}, abstract = {We study offline multi-agent reinforcement learning (RL) in Markov games, where the goal is to learn an approximate equilibrium—such as Nash equilibrium and (Coarse) Correlated Equilibrium—from an offline dataset pre-collected from the game. Existing works consider relatively restricted tabular or linear models and handle each equilibria separately. In this work, we provide the first framework for sample-efficient offline learning in Markov games under general function approximation, handling all 3 equilibria in a unified manner. By using Bellman-consistent pessimism, we obtain interval estimation for policies’ returns, and use both the upper and the lower bounds to obtain a relaxation on the gap of a candidate policy, which becomes our optimization objective. Our results generalize prior works and provide several additional insights. Importantly, we require a data coverage condition that improves over the recently proposed “unilateral concentrability”. Our condition allows selective coverage of deviation policies that optimally trade-off between their greediness (as approximate best responses) and coverage, and we show scenarios where this leads to significantly better guarantees. As a new connection, we also show how our algorithmic framework can subsume seemingly different solution concepts designed for the special case of two-player zero-sum games.} }
Endnote
%0 Conference Paper %T Offline Learning in Markov Games with General Function Approximation %A Yuheng Zhang %A Yu Bai %A Nan Jiang %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-zhang23a %I PMLR %P 40804--40829 %U https://proceedings.mlr.press/v202/zhang23a.html %V 202 %X We study offline multi-agent reinforcement learning (RL) in Markov games, where the goal is to learn an approximate equilibrium—such as Nash equilibrium and (Coarse) Correlated Equilibrium—from an offline dataset pre-collected from the game. Existing works consider relatively restricted tabular or linear models and handle each equilibria separately. In this work, we provide the first framework for sample-efficient offline learning in Markov games under general function approximation, handling all 3 equilibria in a unified manner. By using Bellman-consistent pessimism, we obtain interval estimation for policies’ returns, and use both the upper and the lower bounds to obtain a relaxation on the gap of a candidate policy, which becomes our optimization objective. Our results generalize prior works and provide several additional insights. Importantly, we require a data coverage condition that improves over the recently proposed “unilateral concentrability”. Our condition allows selective coverage of deviation policies that optimally trade-off between their greediness (as approximate best responses) and coverage, and we show scenarios where this leads to significantly better guarantees. As a new connection, we also show how our algorithmic framework can subsume seemingly different solution concepts designed for the special case of two-player zero-sum games.
APA
Zhang, Y., Bai, Y. & Jiang, N.. (2023). Offline Learning in Markov Games with General Function Approximation. Proceedings of the 40th International Conference on Machine Learning, in Proceedings of Machine Learning Research 202:40804-40829 Available from https://proceedings.mlr.press/v202/zhang23a.html.

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