Solving Large Imperfect Information Games Using CFR+

TL;DR

Solving large imperfect information games like poker requires approximate Nash equilibria. The paper introduces CFR$^+$, a CFR-like algorithm that uses regret-matching$^+$ in a vector-form, alternating update scheme, and removes the need for strategy averaging to converge. It reports more than an order of magnitude reduction in convergence time versus vanilla CFR in tests on one-card poker and NL Hold'em subgames, with additional potential memory savings via compressibility. The work also highlights future directions for mathematical analysis and compression techniques.

Abstract

Counterfactual Regret Minimization and variants (e.g. Public Chance Sampling CFR and Pure CFR) have been known as the best approaches for creating approximate Nash equilibrium solutions for imperfect information games such as poker. This paper introduces CFR$^+$, a new algorithm that typically outperforms the previously known algorithms by an order of magnitude or more in terms of computation time while also potentially requiring less memory.

Figures (1)

• Figure 1: One-card poker iterations vs. deck size