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.

翻译：在线学习算法常面临一个基本的三难困境：在对抗性与随机性场景间的遗憾界权衡，以及针对固定比较器的基线安全性。尽管现有方法能在其中一两个领域表现出色，但通常无法在不牺牲最优速率或需要先知式访问问题相关参数的前提下统一所有三个目标。在本工作中，我们通过引入COMPASS-Hedge弥合了这一鸿沟。据我们所知，我们的算法是首个全信息任意时间方法，能同时实现（至多对数因子）：i) 对抗环境中的极小化最优遗憾；ii) 随机环境中基于间隔的实例最优遗憾；iii) 相对于指定基线策略的 $\tilde{\mathcal{O}}(1)$ 遗憾。关键在于，COMPASS-Hedge无需参数且无需预先了解环境性质或随机次优性间隔的幅度。我们的方法依赖于自适应伪遗憾缩放与基于阶段的激进策略的新颖整合，并结合了比较器感知的混合策略。据我们所知，这提供了全信息设置下首个"三世界最优"保证，证明基线安全性无需以牺牲最坏情况鲁棒性或随机环境效率为代价。