Abstract:Online learning algorithms often face 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. To the best of our knowledge, our algorithm is the first full-information anytime method to simultaneously achieve, up to logarithmic factors: 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. Crucially, COMPASS-Hedge is parameter-free and requires no prior knowledge of the environment's nature or the magnitude of the stochastic suboptimality 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.
From: Ting Hu [view email]
[v1]
Sun, 22 Mar 2026 04:17:43 UTC (1,167 KB)
[v2]
Fri, 27 Mar 2026 16:39:05 UTC (1,167 KB)
[v3]
Fri, 22 May 2026 08:52:43 UTC (4,917 KB)
[v4]
Thu, 28 May 2026 07:22:08 UTC (4,917 KB)
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