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

2025-06-05

AI Summary

This paper studies uncoupled accelerated no-regret learning in general games, unifying treatment of both self-play and adversarial settings. We propose the Cautious Optimism meta-algorithm, which introduces the first adaptive pacing framework for non-monotonic step sizes, enabling plug-and-play control of any Follow-the-Regularized-Leader (FTRL) instance. While preserving full uncoupledness—requiring neither inter-player communication nor knowledge of utilities—the algorithm achieves near-optimal regret bounds: $O(log T)$ in self-play, yielding the first theoretical guarantee of near-constant regret in this setting, and $O(sqrt{T})$ in adversarial environments, matching the known lower bound. The method relies only on lightweight online computation, significantly outperforming existing coupled or setting-specific approaches.

Technology Category

• Game Theory and Economic Paradigms: Adversarial Learning
• Machine Learning: Online Learning & Bandits
• Search and Optimization: Adversarial Search

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

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.

Problem

• Accelerates no-regret learning in general games
• Adaptively paces FTRL with minimal overhead
• Achieves near-optimal regret in diverse scenarios

Innovation

• Adaptive pacing for no-regret learning acceleration
• Cautious Optimism framework for FTRL acceleration
• Near-optimal regret in diverse self-play scenarios