# Multiplicative Optimism for Constant Regret in Games

arXiv: https://arxiv.org/abs/2609.21976 · HTML: https://mlsanity.com/paper/2609.21976/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- First posted on arXiv 18 Sep 2026.

## Abstract (arXiv)

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(√ 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(√Tlog d) regret in the face of adversarial utilities.