Solving Imperfect-Information Games via Discounted Regret Minimization


  • Noam Brown Carnegie Mellon University
  • Tuomas Sandholm Carnegie Mellon University



Counterfactual regret minimization (CFR) is a family of iterative algorithms that are the most popular and, in practice, fastest approach to approximately solving large imperfectinformation 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-informationgame pruning techniques and one is also compatible with sampling in the game tree.




How to Cite

Brown, N., & Sandholm, T. (2019). Solving Imperfect-Information Games via Discounted Regret Minimization. Proceedings of the AAAI Conference on Artificial Intelligence, 33(01), 1829-1836.



AAAI Technical Track: Game Theory and Economic Paradigms