No-Regret Learning in Time-Varying Zero-Sum Games

Mengxiao Zhang, Peng Zhao, Haipeng Luo, Zhi-Hua Zhou
Proceedings of the 39th International Conference on Machine Learning, PMLR 162:26772-26808, 2022.

Abstract

Learning from repeated play in a fixed two-player zero-sum game is a classic problem in game theory and online learning. We consider a variant of this problem where the game payoff matrix changes over time, possibly in an adversarial manner. We first present three performance measures to guide the algorithmic design for this problem: 1) the well-studied individual regret, 2) an extension of duality gap, and 3) a new measure called dynamic Nash Equilibrium regret, which quantifies the cumulative difference between the player’s payoff and the minimax game value. Next, we develop a single parameter-free algorithm that simultaneously enjoys favorable guarantees under all these three performance measures. These guarantees are adaptive to different non-stationarity measures of the payoff matrices and, importantly, recover the best known results when the payoff matrix is fixed. Our algorithm is based on a two-layer structure with a meta-algorithm learning over a group of black-box base-learners satisfying a certain property, along with several novel ingredients specifically designed for the time-varying game setting. Empirical results further validate the effectiveness of our algorithm.

Cite this Paper

BibTeX
@InProceedings{pmlr-v162-zhang22an, title = {No-Regret Learning in Time-Varying Zero-Sum Games}, author = {Zhang, Mengxiao and Zhao, Peng and Luo, Haipeng and Zhou, Zhi-Hua}, booktitle = {Proceedings of the 39th International Conference on Machine Learning}, pages = {26772--26808}, year = {2022}, editor = {Chaudhuri, Kamalika and Jegelka, Stefanie and Song, Le and Szepesvari, Csaba and Niu, Gang and Sabato, Sivan}, volume = {162}, series = {Proceedings of Machine Learning Research}, month = {17--23 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v162/zhang22an/zhang22an.pdf}, url = {https://proceedings.mlr.press/v162/zhang22an.html}, abstract = {Learning from repeated play in a fixed two-player zero-sum game is a classic problem in game theory and online learning. We consider a variant of this problem where the game payoff matrix changes over time, possibly in an adversarial manner. We first present three performance measures to guide the algorithmic design for this problem: 1) the well-studied individual regret, 2) an extension of duality gap, and 3) a new measure called dynamic Nash Equilibrium regret, which quantifies the cumulative difference between the player’s payoff and the minimax game value. Next, we develop a single parameter-free algorithm that simultaneously enjoys favorable guarantees under all these three performance measures. These guarantees are adaptive to different non-stationarity measures of the payoff matrices and, importantly, recover the best known results when the payoff matrix is fixed. Our algorithm is based on a two-layer structure with a meta-algorithm learning over a group of black-box base-learners satisfying a certain property, along with several novel ingredients specifically designed for the time-varying game setting. Empirical results further validate the effectiveness of our algorithm.} }
Endnote
%0 Conference Paper %T No-Regret Learning in Time-Varying Zero-Sum Games %A Mengxiao Zhang %A Peng Zhao %A Haipeng Luo %A Zhi-Hua Zhou %B Proceedings of the 39th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2022 %E Kamalika Chaudhuri %E Stefanie Jegelka %E Le Song %E Csaba Szepesvari %E Gang Niu %E Sivan Sabato %F pmlr-v162-zhang22an %I PMLR %P 26772--26808 %U https://proceedings.mlr.press/v162/zhang22an.html %V 162 %X Learning from repeated play in a fixed two-player zero-sum game is a classic problem in game theory and online learning. We consider a variant of this problem where the game payoff matrix changes over time, possibly in an adversarial manner. We first present three performance measures to guide the algorithmic design for this problem: 1) the well-studied individual regret, 2) an extension of duality gap, and 3) a new measure called dynamic Nash Equilibrium regret, which quantifies the cumulative difference between the player’s payoff and the minimax game value. Next, we develop a single parameter-free algorithm that simultaneously enjoys favorable guarantees under all these three performance measures. These guarantees are adaptive to different non-stationarity measures of the payoff matrices and, importantly, recover the best known results when the payoff matrix is fixed. Our algorithm is based on a two-layer structure with a meta-algorithm learning over a group of black-box base-learners satisfying a certain property, along with several novel ingredients specifically designed for the time-varying game setting. Empirical results further validate the effectiveness of our algorithm.
APA
Zhang, M., Zhao, P., Luo, H. & Zhou, Z.. (2022). No-Regret Learning in Time-Varying Zero-Sum Games. Proceedings of the 39th International Conference on Machine Learning, in Proceedings of Machine Learning Research 162:26772-26808 Available from https://proceedings.mlr.press/v162/zhang22an.html.

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