Adapting to game trees in zero-sum imperfect information games
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Imperfect information games (IIG) are games in which each player only partially observes the current game state. We study how to learn ϵ-optimal strategies in a zero-sum IIG through self-play with trajectory feedback. We give a problem-independent lower bound 𝒪(H(A_𝒳+B_𝒴)/ϵ^2) on the required number of realizations to learn these strategies with high probability, where H is the length of the game, A_𝒳 and B_𝒴 are the total number of actions for the two players. We also propose two Follow the Regularize 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 𝒪(H^2(A_𝒳+B_𝒴)/ϵ^2) plays without this requirement by progressively adapting the regularization to the observations.
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