Constant regret in general games via higher-order optimism

Abstract:We introduce an uncoupled learning algorithm which, when employed by all players of an arbitrary $N$-player normal form game with up to $K$ actions per player, guarantees $O(N^3\log^2 K)$ individual regret, uniformly over the horizon of play. The proposed algorithm - which we call higher-order optimism with discounting (HOOD) is a variant of optimistic follow-the-regularized-leader (OptFTRL) that combines a discounted $(N+1)$-th order predictor with entropic regularization over a suitable "lifting" of the game's strategy space. This combination of ingredients is purposefully designed to dampen large oscillations of the induced sequence of play in a controlled manner, removing in this way a key stumbling block of previous attempts to achieve constant regret in general games. Our approach bears several striking similarities to the concurrent - and completely independent - work of Liu, Farina, and Ozdaglar (arXiv:2608.31166), who very recently derived an $O(N^{21}\log^{4} K)$ regret bound through the use of higher-order optimism and an exponential moving average estimator.

Machine Learning (cs.LG); Computer Science and Game Theory (cs.GT)

arXiv:2609.04113 [cs.LG]

(or arXiv:2609.04113v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2609.04113 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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