COMPASS-Hedge: Learning Safely Without Knowing the World

2026-03-22

AI Summary

This work addresses the challenge of simultaneously achieving worst-case robustness in adversarial environments, instance optimality in stochastic settings, and safety relative to a baseline policy in full-information online learning. The paper proposes a fully parameter-free algorithm that, without prior knowledge of the environment type or suboptimality gaps, integrates adaptive pseudo-regret scaling, phased aggressive exploration, and a baseline-aware mixing mechanism within a unified framework. This approach delivers threefold guarantees: minimax-optimal regret in adversarial regimes, instance-optimal regret in stochastic regimes, and Õ(1) safety regret—relative to any fixed baseline—with only a logarithmic factor degradation. To the best of our knowledge, this is the first algorithm in the full-information setting to achieve such “triple optimality” without requiring any environmental assumptions or tuning parameters.

Technology Category

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

Application Category

• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• 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

Abstract

Online learning algorithms often faces a fundamental trilemma: balancing regret guarantees between adversarial and stochastic settings and providing baseline safety against a fixed comparator. While existing methods excel in one or two of these regimes, they typically fail to unify all three without sacrificing optimal rates or requiring oracle access to problem-dependent parameters. In this work, we bridge this gap by introducing COMPASS-Hedge. Our algorithm is the first full-information method to simultaneously achieve: i) Minimax-optimal regret in adversarial environments; ii) Instance-optimal, gap-dependent regret in stochastic environments; and iii) $\tilde{\mathcal{O}}(1)$ regret relative to a designated baseline policy, up to logarithmic factors. Crucially, COMPASS-Hedge is parameter-free and requires no prior knowledge of the environment's nature or the magnitude of the stochastic sub optimality gaps. Our approach hinges on a novel integration of adaptive pseudo-regret scaling and phase-based aggression, coupled with a comparator-aware mixing strategy. To the best of our knowledge, this provides the first "best-of-three-world" guarantee in the full-information setting, establishing that baseline safety does not have to come at the cost of worst-case robustness or stochastic efficiency.

Problem

• online learning
• regret minimization
• baseline safety
• adversarial environment
• stochastic environment

Innovation

• parameter-free online learning
• best-of-three-world
• baseline safety
• adaptive regret scaling
• full-information setting