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：本文解决了从波段反馈中学习不完美信息扩展式博弈时设计近最优算法的开放性问题。我们提出了首个算法系列，仅需$\widetilde{\mathcal{O}}((XA+YB)/\varepsilon^2)$局对弈即可在两人零和博弈中找到$\varepsilon$-近似纳什均衡，其中$X,Y$为两位玩家的信息集数量，$A,B$为他们的动作数量。这相较已知最优样本复杂度$\widetilde{\mathcal{O}}((X^2A+Y^2B)/\varepsilon^2)$实现了$\widetilde{\mathcal{O}}(\max\{X, Y\})$倍的改进，并在对数因子内匹配了信息论下界。通过两种新算法——平衡在线镜像下降和平衡反事实遗憾最小化——我们实现了该样本复杂度。这两种算法均依赖于将\textit{平衡探索策略}创新性地集成到其经典对应算法中。我们还将结果扩展至多人一般和博弈中粗相关均衡的学习。