Solving Large Sequential Games With The Excessive Gap Technique

Authors:
Christian Kroer Faceook, Core Data Science
Gabriele Farina Carnegie Mellon University
Tuomas Sandholm Carnegie Mellon University

Introduction:

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.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.

Abstract:

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. \emph{First-order methods} have significantly better theoretical convergence rates than any \emph{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 \emph{excessive gap technique}---instantiated with the \emph{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 \emph{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.

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