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Adapting to game trees in zero-sum imperfect information games
Côme Fiegel · Pierre Menard · Tadashi Kozuno · Remi Munos · Vianney Perchet · Michal Valko

Wed Jul 26 07:08 PM -- 07:16 PM (PDT) @ Ballroom A
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.

Author Information

Côme Fiegel (CREST-ENSAE)
Pierre Menard (ENS Lyon)
Tadashi Kozuno (Omron Sinic X)
Remi Munos (DeepMind)
Vianney Perchet (ENS Paris-Saclay & Criteo AI Lab)
Michal Valko (Google DeepMind / Inria / MVA)

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