Minimizing Weighted Counterfactual Regret with Optimistic Online Mirror Descent

Counterfactual regret minimization (CFR) is a family of algorithms for effectively solving imperfect-information games. It decomposes the total regret into counterfactual regrets, utilizing local regret minimization algorithms, such as Regret Matching (RM) or RM+, to minimize them. Recent research establishes a connection between Online Mirror Descent (OMD) and RM+, paving the way for an optimistic variant PRM+ and its extension PCFR+. However, PCFR+ assigns uniform weights for each iteration when determining regrets, leading to substantial regrets when facing dominated actions. This work explores minimizing weighted counterfactual regret with optimistic OMD, resulting in a novel CFR variant PDCFR+. It integrates PCFR+ and Discounted CFR (DCFR) in a principled manner, swiftly mitigating negative effects of dominated actions and consistently leveraging predictions to accelerate convergence. Theoretical analyses prove that PDCFR+ converges to a Nash equilibrium, particularly under distinct weighting schemes for regrets and average strategies. Experimental results demonstrate PDCFR+'s fast convergence in common imperfect-information games. The code is available at https://github.com/rpSebastian/PDCFRPlus.