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.

翻译：本文解决从私有反馈学习不完美信息博弈的近最优算法设计的问题。我们提出了第一条算法线路，仅需要 $\widetilde{\mathcal{O}}((XA+YB)/\varepsilon^2)$ 次游戏来在两人零和游戏中找到一个 $\varepsilon$-近似纳什均衡。其中，$X,Y$ 是信息集的数量，$A,B$ 是两个玩家的可行动作的数量。这比已知最优样本复杂度 $\widetilde{\mathcal{O}}((X^2A+Y^2B)/\varepsilon^2)$ 提高了 $\widetilde{\mathcal{O}}(\max\{X,Y\})$ 的因子，且能够达到信息论的下界，相差对数因子。我们通过两种新算法来实现这种样本复杂度：平衡的在线镜像下降 和 平衡的可逆选择后悔最小化。两种算法都依赖于将平衡的探索策略集成到其经典对应方法中的新方法。我们还将我们的结果扩展到了多人常规和游戏中学习粗略相关均衡。