Regret Minimization in Games with Incomplete Information

Extensive games are a powerful model of multiagent decision-making scenarioswith incomplete information. Finding a Nash equilibrium for very large instancesof these games has received a great deal of recent attention. In this paper, wedescribe a new technique for solving large games based on regret minimization.In particular, we introduce the notion of counterfactual regret, which exploits thedegree of incomplete information in an extensive game. We show howminimizingcounterfactual regret minimizes overall regret, and therefore in self-play can beused to compute a Nash equilibrium. We demonstrate this technique in the domainof poker, showing we can solve abstractions of limit Texas Hold’em with as manyas 10 states, two orders of magnitude larger than previous methods.