Efficient Predictive Counterfactual Regret Minimization$^+$ Algorithm in Solving Extensive-Form Games
Keywords: Imperfect-Information Extensive-Form Games, Nash Equilibrium, Counterfactual Regret Minimization
TL;DR: We propose P2PCFR$^+$, a novel and effective varaint of PCFR$^+$, achiving faster empirical convergence rate than existing PCFR$^+$ variants.
Abstract: Imperfect-information extensive-form games (IIGs) serve as a foundational model for capturing interactions among multiple agents in sequential settings with hidden information. A common objective of IIGs is to calculate a Nash equilibrium (NE). Counterfactual Regret Minimization (CFR) algorithms have been widely developed to learn an NE in two-player zero-sum IIGs. Among CFR algorithms, Predictive CFR$^+$ (PCFR$^+$) is powerful, usually achieving an extremely fast empirical convergence rate. However, PCFR$^+$ suffers from the significant discrepancy between strategies represented by explicit accumulated counterfactual regrets across two consecutive iterations, which decreases the empirical convergence rate of PCFR$^+$ in practice. To mitigate this significant discrepancy, we introduce a novel and effective variant of PCFR$^+$, termed Pessimistic PCFR$^+$ (P2PCFR$^+$), minimizing the discrepancy between strategies represented by implicit and explicit accumulated regrets within the same iteration. We provide theoretical proof to show that P2PCFR$^+$ exhibits a faster theoretical convergence rate than PCFR$^+$. Experimental results demonstrate that P2PCFR$^+$ outperforms other tested CFR variants.
Primary Area: other topics in machine learning (i.e., none of the above)
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Submission Number: 10720
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