CMWU achieves constant regret ofln(m)/η in all normal-form games with m actions and fixed step-sizesη.

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-ofthe-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.

In'00: Revised the Second International Conferenceon Computersand Games333-345, 2000.

Aconceptually appealing approach forlearning Extensive-FormGames (EFGs) is to convert them to Normal-Form Games (NFGs).

However, directly applying existing subgame solving techniques may be difficult, due to the intricate nature and substantial size of many real-world games.

Can we predict how well a team of individuals will perform together?