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Life sciences · Preprint
arXiv · September 3, 2026
Posted before peer review. The findings may change or fail to hold.
This is an unrefereed preprint in game-theoretic algorithm design, not a clinical or empirical study. The authors propose HOOD, a variant of optimistic follow-the-regularized-leader, claiming to achieve O(N³log²K) individual regret in N-player normal form games, and note concurrent work by Liu, Farina, and Ozdaglar achieving a weaker O(N²¹log⁴K) bound. The work is purely theoretical with no empirical or clinical validation.
Preprint.
HOOD algorithm achieves O(N³log²K) individual regret uniformly over the horizon in N-player normal form games with up to K actions per player Concurrent independent work by Liu, Farina, and Ozdaglar derived O(N²¹log⁴K) regret bound using higher-order optimism and exponential moving average estimator
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This is an unrefereed theoretical computer science preprint presenting a novel algorithmic result in game theory; it has not undergone peer review and lacks empirical validation or clinical application.
Quoted from the source exactly as published.
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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.
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