Counterfactual regret minimization (CFR) is a family of iterative algorithms showing promising results in solving imperfect-information games. Recent novel CFR variants (e.g., CFR+, DCFR) have significantly improved the convergence rate of the vanilla CFR. The key to these CFR variants’ performance is weighting each iteration non-uniformly, i.e., discounting earlier iterations. However, these algorithms use a fixed, manually-specified scheme to weight each iteration, which enormously limits their potential. In this work, we propose Dynamic Discounted CFR (DDCFR), the first equilibrium-finding framework that discounts prior iterations using a dynamic, automatically-learned scheme. We formalize CFR’s iteration process as a carefully designed Markov decision process and transform the discounting scheme learning problem into a policy optimization problem within it. The learned discounting scheme dynamically weights each iteration on the fly using information available at runtime. Experimental results across multiple games demonstrate that DDCFR’s dynamic discounting scheme has a strong generalization ability and leads to faster convergence with improved performance.
Dynamic Discounted Counterfactual Regret Minimization
Hang Xu Kai Li Haobo Fu QIANG FU Junliang Xing Jian Cheng