Adapting to game trees in zero-sum imperfect information games

Côme Fiegel, Pierre Menard, Tadashi Kozuno, Remi Munos, Vianney Perchet, Michal Valko
Proceedings of the 40th International Conference on Machine Learning, PMLR 202:10093-10135, 2023.

Abstract

Imperfect information games (IIG) are games in which each player only partially observes the current game state. We study how to learn $\epsilon$-optimal strategies in a zero-sum IIG through self-play with trajectory feedback. We give a problem-independent lower bound $\widetilde{\mathcal{O}}(H(A_{\mathcal{X}}+B_{\mathcal{Y}})/\epsilon^2)$ on the required number of realizations to learn these strategies with high probability, where $H$ is the length of the game, $A_{\mathcal{X}}$ and $B_{\mathcal{Y}}$ are the total number of actions for the two players. We also propose two Follow the Regularized leader (FTRL) algorithms for this setting: Balanced FTRL which matches this lower bound, but requires the knowledge of the information set structure beforehand to define the regularization; and Adaptive FTRL which needs $\widetilde{\mathcal{O}}(H^2(A_{\mathcal{X}}+B_{\mathcal{Y}})/\epsilon^2)$ realizations without this requirement by progressively adapting the regularization to the observations.

Cite this Paper

BibTeX
@InProceedings{pmlr-v202-fiegel23a, title = {Adapting to game trees in zero-sum imperfect information games}, author = {Fiegel, C\^{o}me and Menard, Pierre and Kozuno, Tadashi and Munos, Remi and Perchet, Vianney and Valko, Michal}, booktitle = {Proceedings of the 40th International Conference on Machine Learning}, pages = {10093--10135}, 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/fiegel23a/fiegel23a.pdf}, url = {https://proceedings.mlr.press/v202/fiegel23a.html}, abstract = {Imperfect information games (IIG) are games in which each player only partially observes the current game state. We study how to learn $\epsilon$-optimal strategies in a zero-sum IIG through self-play with trajectory feedback. We give a problem-independent lower bound $\widetilde{\mathcal{O}}(H(A_{\mathcal{X}}+B_{\mathcal{Y}})/\epsilon^2)$ on the required number of realizations to learn these strategies with high probability, where $H$ is the length of the game, $A_{\mathcal{X}}$ and $B_{\mathcal{Y}}$ are the total number of actions for the two players. We also propose two Follow the Regularized leader (FTRL) algorithms for this setting: Balanced FTRL which matches this lower bound, but requires the knowledge of the information set structure beforehand to define the regularization; and Adaptive FTRL which needs $\widetilde{\mathcal{O}}(H^2(A_{\mathcal{X}}+B_{\mathcal{Y}})/\epsilon^2)$ realizations without this requirement by progressively adapting the regularization to the observations.} }
Endnote
%0 Conference Paper %T Adapting to game trees in zero-sum imperfect information games %A Côme Fiegel %A Pierre Menard %A Tadashi Kozuno %A Remi Munos %A Vianney Perchet %A Michal Valko %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-fiegel23a %I PMLR %P 10093--10135 %U https://proceedings.mlr.press/v202/fiegel23a.html %V 202 %X Imperfect information games (IIG) are games in which each player only partially observes the current game state. We study how to learn $\epsilon$-optimal strategies in a zero-sum IIG through self-play with trajectory feedback. We give a problem-independent lower bound $\widetilde{\mathcal{O}}(H(A_{\mathcal{X}}+B_{\mathcal{Y}})/\epsilon^2)$ on the required number of realizations to learn these strategies with high probability, where $H$ is the length of the game, $A_{\mathcal{X}}$ and $B_{\mathcal{Y}}$ are the total number of actions for the two players. We also propose two Follow the Regularized leader (FTRL) algorithms for this setting: Balanced FTRL which matches this lower bound, but requires the knowledge of the information set structure beforehand to define the regularization; and Adaptive FTRL which needs $\widetilde{\mathcal{O}}(H^2(A_{\mathcal{X}}+B_{\mathcal{Y}})/\epsilon^2)$ realizations without this requirement by progressively adapting the regularization to the observations.
APA
Fiegel, C., Menard, P., Kozuno, T., Munos, R., Perchet, V. & Valko, M.. (2023). Adapting to game trees in zero-sum imperfect information games. Proceedings of the 40th International Conference on Machine Learning, in Proceedings of Machine Learning Research 202:10093-10135 Available from https://proceedings.mlr.press/v202/fiegel23a.html.

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