Cautious Optimism: A Meta-Algorithm for Near-Constant Regret in General Games

• URL: http://arxiv.org/abs/2506.05005v1
• Date: Thu, 05 Jun 2025 13:13:48 GMT
• Title: Cautious Optimism: A Meta-Algorithm for Near-Constant Regret in General Games
• Authors: Ashkan Soleymani, Georgios Piliouras, Gabriele Farina,
• Abstract summary: We show that no-regret learning acceleration through adaptive pacing of the learners is not an isolated phenomenon.<n>We introduce emphCautious Optimism, a framework for substantially faster regularized learning in general games.
• Score: 46.462843198107144
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Recent work [Soleymani et al., 2025] introduced a variant of Optimistic Multiplicative Weights Updates (OMWU) that adaptively controls the learning pace in a dynamic, non-monotone manner, achieving new state-of-the-art regret minimization guarantees in general games. In this work, we demonstrate that no-regret learning acceleration through adaptive pacing of the learners is not an isolated phenomenon. We introduce \emph{Cautious Optimism}, a framework for substantially faster regularized learning in general games. Cautious Optimism takes as input any instance of Follow-the-Regularized-Leader (FTRL) and outputs an accelerated no-regret learning algorithm by pacing the underlying FTRL with minimal computational overhead. Importantly, we retain uncoupledness (learners do not need to know other players' utilities). Cautious Optimistic FTRL achieves near-optimal $O_T(\log T)$ regret in diverse self-play (mixing-and-matching regularizers) while preserving the optimal $O(\sqrt{T})$ regret in adversarial scenarios. In contrast to prior works (e.g. Syrgkanis et al. [2015], Daskalakis et al. [2021]), our analysis does not rely on monotonic step-sizes, showcasing a novel route for fast learning in general games.

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