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：本文解决了在赌徒反馈下从不完美信息扩展式博弈中进行近似最优算法设计的开放性问题。我们提出了首个算法系列，仅需$\widetilde{\mathcal{O}}((XA+YB)/\varepsilon^2)$次博弈回合即可在两人零和博弈中找到$\varepsilon$-近似纳什均衡，其中$X,Y$分别为两位玩家的信息集数量，$A,B$为他们的行动数量。该结果将已知最优样本复杂度$\widetilde{\mathcal{O}}((X^2A+Y^2B)/\varepsilon^2)$降低了$\widetilde{\mathcal{O}}(\max\{X, Y\})$倍，并达到信息论下界（仅差对数因子）。我们通过两种新算法实现该样本复杂度：平衡在线镜像下降法与平衡反事实遗憾最小化法。两种算法均依赖创新方法——将 \emph{平衡探索策略} 集成至经典算法框架中。此外，我们将结果推广至多人一般和博弈中的粗相关均衡学习。