Multiplicative Optimism for Constant Regret in Games

Abstract:We introduce Multiplicatively Optimistic Regret Matching (MORM), an uncoupled learning rule for finite general-sum games. Under simultaneous full-information self-play, every player achieves external regret $O(\sqrt n\log d)$ uniformly over all horizons, using only one-step optimism. The analysis combines a potential-based regret-matching argument with multiplicative stability and Hellinger control of strategy movement. A learning-rate safeguard additionally gives $O(\sqrt{T\log d})$ regret in the face of adversarial utilities.

Computer Science and Game Theory (cs.GT); Machine Learning (cs.LG); Optimization and Control (math.OC)

arXiv:2609.21976 [cs.GT]

(or arXiv:2609.21976v1 [cs.GT] for this version)

https://doi.org/10.48550/arXiv.2609.21976 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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