Solving Large Sequential Games with the Excessive Gap Technique
This work addresses the practical inefficiency of first-order methods in large-scale imperfect-information games, enabling competitive performance with established CFR methods in real-world applications like poker AI.
The paper tackled the gap between theoretical convergence rates and practical performance in solving large sequential games by applying a first-order method, the excessive gap technique with dilated entropy, to efficiently solve large real-world poker endgames competitively with CFR variants.
There has been tremendous recent progress on equilibrium-finding algorithms for zero-sum imperfect-information extensive-form games, but there has been a puzzling gap between theory and practice. First-order methods have significantly better theoretical convergence rates than any counterfactual-regret minimization (CFR) variant. Despite this, CFR variants have been favored in practice. Experiments with first-order methods have only been conducted on small- and medium-sized games because those methods are complicated to implement in this setting, and because CFR variants have been enhanced extensively for over a decade they perform well in practice. In this paper we show that a particular first-order method, a state-of-the-art variant of the excessive gap technique---instantiated with the dilated entropy distance function---can efficiently solve large real-world problems competitively with CFR and its variants. We show this on large endgames encountered by the Libratus poker AI, which recently beat top human poker specialist professionals at no-limit Texas hold'em. We show experimental results on our variant of the excessive gap technique as well as a prior version. We introduce a numerically friendly implementation of the smoothed best response computation associated with first-order methods for extensive-form game solving. We present, to our knowledge, the first GPU implementation of a first-order method for extensive-form games. We present comparisons of several excessive gap technique and CFR variants.