Abstract Extensive-form games (EFGs) model finite sequential interactions between players. The amount of memory required to represent these games is the main bottleneck of algorithms for computing optimal strategies and the size of these strategies is often impractical for real-world applications. A common approach to tackle the memory bottleneck is to use information abstraction that removes parts of information available to players thus reducing the number of decision points in the game. However, existing information-abstraction techniques are either specific for a particular domain, they do not provide any quality guarantees, or they are applicable to very small subclasses of EFGs. We present domain-independent abstraction methods for creating imperfect recall abstractions in extensive-form games that allow computing strategies that are (near) optimal in the original game. To this end, we introduce two novel algorithms, FPIRA and CFR+IRA, based on fictitious play and counterfactual regret minimization. These algorithms can start with an arbitrary domain specific, or the coarsest possible, abstraction of the original game. The algorithms iteratively detect the missing information they require for computing a strategy for the abstract game that is (near) optimal in the original game. This information is then included back into the abstract game. Moreover, our algorithms are able to exploit imperfect-recall abstractions that allow players to forget even history of their own actions. However, the algorithms require traversing the complete unabstracted game tree. We experimentally show that our algorithms can closely approximate Nash equilibrium of large games using abstraction with as little as 0.9% of information sets of the original game. Moreover, the results suggest that memory savings increase with the increasing size of the original games.

中文翻译：

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在扩展形式游戏中自动构建有界损失不完美回忆抽象

摘要 扩展形式博弈 (EFG) 对玩家之间的有限顺序交互进行建模。表示这些游戏所需的内存量是计算最优策略的算法的主要瓶颈，而这些策略的大小对于现实世界的应用程序来说通常是不切实际的。解决内存瓶颈的常用方法是使用信息抽象，移除玩家可用的部分信息，从而减少游戏中的决策点数量。然而，现有的信息抽象技术要么特定于特定领域，要么不提供任何质量保证，要么适用于非常小的 EFG 子类。我们提出了独立于领域的抽象方法，用于在扩展形式的游戏中创建不完美的召回抽象，允许在原始游戏中（接近）最优的计算策略。为此，我们介绍了两种基于虚构游戏和反事实后悔最小化的新算法 FPIRA 和 CFR+IRA。这些算法可以从原始游戏的任意特定领域或最粗略的抽象开始。算法迭代地检测它们为计算在原始游戏中（接近）最优的抽象游戏的策略所需的缺失信息。然后将这些信息重新包含到抽象游戏中。此外，我们的算法能够利用不完美回忆抽象，让玩家甚至忘记他们自己行为的历史。然而，算法需要遍历完整的非抽象博弈树。我们通过实验表明，我们的算法可以使用原始游戏的 0.9% 的信息集进行抽象，从而非常接近大型游戏的纳什均衡。此外，结果表明内存节省随着原始游戏大小的增加而增加。