Faster Game Solving via Asymmetry of Step Sizes
This work addresses robustness issues in game-solving algorithms for imperfect-information games, which is important for AI applications like poker, but it is incremental as it builds on existing CFR methods.
The paper tackles the problem of unstable performance in Predictive CFR+ (PCFR+) algorithms for solving two-player zero-sum imperfect-information games when predictions are inaccurate, proposing Asymmetric PCFR+ (APCFR+) and a simplified version (SAPCFR+) that use asymmetric step sizes to enhance robustness, with experimental results showing they outperform PCFR+ in most tested games and achieve comparable convergence rates.
Counterfactual Regret Minimization (CFR) algorithms are widely used to compute a Nash equilibrium (NE) in two-player zero-sum imperfect-information extensive-form games (IIGs). Among them, Predictive CFR$^+$ (PCFR$^+$) is particularly powerful, achieving an exceptionally fast empirical convergence rate via the prediction in many games.However, the empirical convergence rate of PCFR$^+$ would significantly degrade if the prediction is inaccurate, leading to unstable performance on certain IIGs. To enhance the robustness of PCFR$^+$, we propose Asymmetric PCFR$^+$ (APCFR$^+$), which employs an adaptive asymmetry of step sizes between the updates of implicit and explicit accumulated counterfactual regrets to mitigate the impact of the prediction inaccuracy on convergence. We present a theoretical analysis demonstrating why APCFR$^+$ can enhance the robustness. To the best of our knowledge, we are the first to propose the asymmetry of step sizes, a simple yet novel technique that effectively improves the robustness of PCFR$^+$. Then, to reduce the difficulty of implementing APCFR$^+$ caused by the adaptive asymmetry, we propose a simplified version of APCFR$^+$ called Simple APCFR$^+$ (SAPCFR$^+$), which uses a fixed asymmetry of step sizes to enable only a single-line modification compared to original PCFR$^+$.Experimental results on five standard IIG benchmarks and two heads-up no-limit Texas Hold' em (HUNL) Subagems show that (i) both APCFR$^+$ and SAPCFR$^+$ outperform PCFR$^+$ in most of the tested games, (ii) SAPCFR$^+$ achieves a comparable empirical convergence rate with APCFR$^+$,and (iii) our approach can be generalized to improve other CFR algorithms, e.g., Discount CFR (DCFR).