Regret Matching+ (RM+) and its variants are important algorithms for solving large-scale games. However, a theoretical understanding of their success in practice is still a mystery. Moreover, recent advances on fast convergence in games are limited to no-regret algorithms such as online mirror descent, which satisfy stability. In this paper, we first give counterexamples showing that RM+ and its predictive version can be unstable, which might cause other players to suffer large regret. We then provide two fixes: restarting and chopping off the positive orthant that RM+ works in. We show that these fixes are sufficient to get $O(T^{1/4})$ individual regret and $O(1)$ social regret in normal-form games via RM+ with predictions. We also apply our stabilizing techniques to clairvoyant updates in the uncoupled learning setting for RM+ and prove desirable results akin to recent works for Clairvoyant online mirror descent. Our experiments show the advantages of our algorithms over vanilla RM+-based algorithms in matrix and extensive-form games.

研究Regret Matching+算法及其变体在解决大规模博弈中的应用，提出稳定化的解决方案，成功获取了在正态型博弈中的个体遗憾和社会遗憾的最优解，并在clairvoyant在线问题解决方面获得了理想结果。

懊悔匹配+: 博弈中的(不)稳定性和快速收敛