Multiplicative Optimism for Constant Regret in Games

arXiv:2609.21976v1 Announce Type: cross 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 nlog 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{Tlog d}) regret in the face of adversarial utilities.

Source: arXiv cs.LG | 2026-09-21