论文标题
与不完美的信息对广泛形式的游戏的近乎最佳学习
Near-Optimal Learning of Extensive-Form Games with Imperfect Information
论文作者
论文摘要
本文解决了设计近乎最佳算法的开放问题，用于学习不完美的信息从匪徒反馈中进行广泛形式的游戏。 We present the first line of algorithms that require only $\widetilde{\mathcal{O}}((XA+YB)/\varepsilon^2)$ episodes of play to find an $\varepsilon$-approximate Nash equilibrium in two-player zero-sum games, where $X,Y$ are the number of information sets and $A,B$ are the number of两个球员的动作。这在$ \ widetilde {\ Mathcal {o}}（（（x^2a+y^2b）/\ varepsilon^2）$的最佳样本复杂性上的改善，其均为$ \ wideTilde {\ natercal {\ Mathcal {o}}（o}}}（\ max \ max \ max \ max \ {x，y \ {x，y \ \ \ \ \ \} $ noction $ noction，我们通过两种新算法实现了这种样本的复杂性：平衡的在线镜像下降和平衡的反事实遗憾最小化。两种算法都依赖于将\ emph {平衡探索策略}整合到其经典对应物中的新方法。我们还将结果扩展到学习多玩家通用和游戏中的粗相关平衡。
This paper resolves the open question of designing near-optimal algorithms for learning imperfect-information extensive-form games from bandit feedback. We present the first line of algorithms that require only $\widetilde{\mathcal{O}}((XA+YB)/\varepsilon^2)$ episodes of play to find an $\varepsilon$-approximate Nash equilibrium in two-player zero-sum games, where $X,Y$ are the number of information sets and $A,B$ are the number of actions for the two players. This improves upon the best known sample complexity of $\widetilde{\mathcal{O}}((X^2A+Y^2B)/\varepsilon^2)$ by a factor of $\widetilde{\mathcal{O}}(\max\{X, Y\})$, and matches the information-theoretic lower bound up to logarithmic factors. We achieve this sample complexity by two new algorithms: Balanced Online Mirror Descent, and Balanced Counterfactual Regret Minimization. Both algorithms rely on novel approaches of integrating \emph{balanced exploration policies} into their classical counterparts. We also extend our results to learning Coarse Correlated Equilibria in multi-player general-sum games.
