论文标题
适应零和不完美的信息游戏中的游戏树
Adapting to game trees in zero-sum imperfect information games
论文作者
论文摘要
不完美的信息游戏（IIG）是每个玩家仅部分观察当前游戏状态的游戏。我们研究如何通过轨迹反馈来学习零和IIG中的$ε$ - 最佳策略。我们给出了一个无关的下限$ \ wideTilde {\ Mathcal {o}}（h（a _ {_ {\ Mathcal {x}}}+b _ {\ Mathcal {y}}}}}}}}}}}}）/ε^2）$在$概率上学习这些策略的数量，在$上是$ H $的长度， $ a _ {\ mathcal {x}} $和$ b _ {\ Mathcal {y}} $是两个玩家的操作总数。我们还建议两个遵循此设置的正规领导者（FTRL）算法：平衡的FTRL匹配此下限，但要求事先了解信息集结构以定义正则化；和需要$ \ widetilde {\ Mathcal {o}}（h^2（A _ {\ Mathcal {X}}}+B _ {\ Mathcal {Y}}}）/〜ph）的自适应ftrl。
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 $\widetilde{\mathcal{O}}(H(A_{\mathcal{X}}+B_{\mathcal{Y}})/ε^2)$ on the required number of realizations to learn these strategies with high probability, where $H$ is the length of the game, $A_{\mathcal{X}}$ 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 $\widetilde{\mathcal{O}}(H^2(A_{\mathcal{X}}+B_{\mathcal{Y}})/ε^2)$ realizations without this requirement by progressively adapting the regularization to the observations.
