Solving Imperfect-Information Games via Discounted Regret Minimization

TL;DR

This paper introduces novel variants of counterfactual regret minimization (CFR) that incorporate discounting, reweighting, and optimistic regret matching, significantly improving performance in solving large imperfect-information games.

Contribution

The paper presents new CFR variants that outperform CFR+ and are compatible with modern pruning and sampling techniques, advancing the state-of-the-art in imperfect-information game solving.

Findings

New CFR variants outperform CFR+ in all tested games.

Some variants are compatible with game pruning techniques.

One variant supports sampling in the game tree.

Abstract

Counterfactual regret minimization (CFR) is a family of iterative algorithms that are the most popular and, in practice, fastest approach to approximately solving large imperfect-information games. In this paper we introduce novel CFR variants that 1) discount regrets from earlier iterations in various ways (in some cases differently for positive and negative regrets), 2) reweight iterations in various ways to obtain the output strategies, 3) use a non-standard regret minimizer and/or 4) leverage "optimistic regret matching". They lead to dramatically improved performance in many settings. For one, we introduce a variant that outperforms CFR+, the prior state-of-the-art algorithm, in every game tested, including large-scale realistic settings. CFR+ is a formidable benchmark: no other algorithm has been able to outperform it. Finally, we show that, unlike CFR+, many of the important new variants are compatible with modern imperfect-information-game pruning techniques and one is also compatible with sampling in the game tree.