Gap-Dependent Bounds for Two-Player Markov Games

Zehao Dou, Zhuoran Yang, Zhaoran Wang, Simon Du
Proceedings of The 25th International Conference on Artificial Intelligence and Statistics, PMLR 151:432-455, 2022.

Abstract

As one of the most popular methods in the field of reinforcement learning, Q-learning has received increasing attention. Recently, there have been more theoretical works on the regret bound of algorithms that belong to the Q-learning class in different settings. In this paper, we analyze the cumulative regret when conducting Nash Q-learning algorithm on 2-player turn-based stochastic Markov games (2-TBSG), and propose the very first gap dependent logarithmic upper bounds in the episodic tabular setting. This bound matches the theoretical lower bound only up to a logarithmic term. Furthermore, we extend the conclusion to the discounted game setting with infinite horizon and propose a similar gap dependent logarithmic regret bound. Also, under the linear MDP assumption, we obtain another logarithmic regret for 2-TBSG, in both centralized and independent settings.

Cite this Paper

BibTeX
@InProceedings{pmlr-v151-dou22a, title = { Gap-Dependent Bounds for Two-Player Markov Games }, author = {Dou, Zehao and Yang, Zhuoran and Wang, Zhaoran and Du, Simon}, booktitle = {Proceedings of The 25th International Conference on Artificial Intelligence and Statistics}, pages = {432--455}, year = {2022}, editor = {Camps-Valls, Gustau and Ruiz, Francisco J. R. and Valera, Isabel}, volume = {151}, series = {Proceedings of Machine Learning Research}, month = {28--30 Mar}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v151/dou22a/dou22a.pdf}, url = {https://proceedings.mlr.press/v151/dou22a.html}, abstract = { As one of the most popular methods in the field of reinforcement learning, Q-learning has received increasing attention. Recently, there have been more theoretical works on the regret bound of algorithms that belong to the Q-learning class in different settings. In this paper, we analyze the cumulative regret when conducting Nash Q-learning algorithm on 2-player turn-based stochastic Markov games (2-TBSG), and propose the very first gap dependent logarithmic upper bounds in the episodic tabular setting. This bound matches the theoretical lower bound only up to a logarithmic term. Furthermore, we extend the conclusion to the discounted game setting with infinite horizon and propose a similar gap dependent logarithmic regret bound. Also, under the linear MDP assumption, we obtain another logarithmic regret for 2-TBSG, in both centralized and independent settings. } }
Endnote
%0 Conference Paper %T Gap-Dependent Bounds for Two-Player Markov Games %A Zehao Dou %A Zhuoran Yang %A Zhaoran Wang %A Simon Du %B Proceedings of The 25th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2022 %E Gustau Camps-Valls %E Francisco J. R. Ruiz %E Isabel Valera %F pmlr-v151-dou22a %I PMLR %P 432--455 %U https://proceedings.mlr.press/v151/dou22a.html %V 151 %X As one of the most popular methods in the field of reinforcement learning, Q-learning has received increasing attention. Recently, there have been more theoretical works on the regret bound of algorithms that belong to the Q-learning class in different settings. In this paper, we analyze the cumulative regret when conducting Nash Q-learning algorithm on 2-player turn-based stochastic Markov games (2-TBSG), and propose the very first gap dependent logarithmic upper bounds in the episodic tabular setting. This bound matches the theoretical lower bound only up to a logarithmic term. Furthermore, we extend the conclusion to the discounted game setting with infinite horizon and propose a similar gap dependent logarithmic regret bound. Also, under the linear MDP assumption, we obtain another logarithmic regret for 2-TBSG, in both centralized and independent settings.
APA
Dou, Z., Yang, Z., Wang, Z. & Du, S.. (2022). Gap-Dependent Bounds for Two-Player Markov Games . Proceedings of The 25th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 151:432-455 Available from https://proceedings.mlr.press/v151/dou22a.html.

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