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arXiv · 2305.14709

Regret Matching+: (In)Stability and Fast Convergence in Games

Gabriele Farina·Julien Grand-Clément·Christian Kroer·Chung-Wei Lee·Haipeng Luo
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Abstract

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.

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Gabriele Farina, Julien Grand-Clément, Christian Kroer, Chung-Wei Lee, Haipeng Luo. 2023-05-24. Regret Matching+: (In)Stability and Fast Convergence in Games. https://arxiv.org/abs/2305.14709

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