Potential-aware imperfect-recall abstraction with earth mover's distance in imperfect-information games

Abstract

There is often a large disparity between the size of a game we wish to solve and the size of the largest instances solva ble by the best algorithms; for example, a popular variant of poker has about 1O'° nodes in its game tree, while the currently best approximate equilibrium-finding algorithms scale to games with around 1012 nodes. In order to approxi mate equilibrium strategies in these games, the leading app roach is to create a sufficiently small strategic approxirnar ico of the full gamc, called an abstraction, and to solve that smaller game instead. The leading abstraction algorithm for imperfect-information games generates abstractions that have imperfect recall and are distribution aware, using k-means with the earth mover's distance metric to cluster similar states together. A distribution-aware abstraction groups states tog ether at a given round if their full distributions over future strength arc similar (as opposed to. for example. just the exp ectation of their strength). The leading algorithm conside rs distributions over future strength at the final round of the game. However, one might benefit by considering the traject ory of distributions over strength in all future rounds, not just the final round. An abstraction algorithm that takes all fut ure rounds into account is called potential aware. We present the first algorithm for computing potential-aware imperfect- recall abstractions using earth mover's distance. Experiments on no-limit Texas Hold'em show that our algorithm improves performance oer the previously best approach.