Efficient Last-iterate Convergence Algorithms in Solving Games

• URL: http://arxiv.org/abs/2308.11256v2
• Date: Tue, 18 Mar 2025 08:31:00 GMT
• Title: Efficient Last-iterate Convergence Algorithms in Solving Games
• Authors: Linjian Meng, Youzhi Zhang, Zhenxing Ge, Shangdong Yang, Tianyu Ding, Wenbin Li, Tianpei Yang, Bo An, Yang Gao,
• Abstract summary: Recent studies reformulate learning an NE of the original EFG as learning the NEs of a sequence of (perturbed) regularized EFGs.<n>In this paper, we prove that CFR$+$, a classical parameter-free RM-based CFR algorithm, achieves last-iterate convergence in learning an NE of perturbed regularized EFGs.
• Score: 29.25745562794961
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: To establish last-iterate convergence for Counterfactual Regret Minimization (CFR) algorithms in learning a Nash equilibrium (NE) of extensive-form games (EFGs), recent studies reformulate learning an NE of the original EFG as learning the NEs of a sequence of (perturbed) regularized EFGs. Consequently, proving last-iterate convergence in solving the original EFG reduces to proving last-iterate convergence in solving (perturbed) regularized EFGs. However, the empirical convergence rates of the algorithms in these studies are suboptimal, since they do not utilize Regret Matching (RM)-based CFR algorithms to solve perturbed EFGs, which are known the exceptionally fast empirical convergence rates. Additionally, since solving multiple perturbed regularized EFGs is required, fine-tuning across all such games is infeasible, making parameter-free algorithms highly desirable. In this paper, we prove that CFR$^+$, a classical parameter-free RM-based CFR algorithm, achieves last-iterate convergence in learning an NE of perturbed regularized EFGs. Leveraging CFR$^+$ to solve perturbed regularized EFGs, we get Reward Transformation CFR$^+$ (RTCFR$^+$). Importantly, we extend prior work on the parameter-free property of CFR$^+$, enhancing its stability, which is crucial for the empirical convergence of RTCFR$^+$. Experiments show that RTCFR$^+$ significantly outperforms existing algorithms with theoretical last-iterate convergence guarantees.

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