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三元困境：在对抗性与随机性设定间权衡遗憾界，并提供相对于固定比较器的基准安全性。尽管现有方法在一或两个领域表现优异，但它们通常无法在无需牺牲最优速率或需要问题依赖参数预言机访问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填补了这一空白。据我们所知，我们的算法是首个同时实现如下目标的全信息实时方法（对数因子内）：i）对抗性环境下极小化最优遗憾；ii）随机环境下实例最优、间隙依赖遗憾；iii）相对于指定基准策略的$\tilde{\mathcal{O}}(1)$遗憾。关键的是，COMPASS-Hedge是无参数算法，无需环境性质或随机次优间隙幅度的先验知识。我们的方法基于自适应伪遗憾缩放与分阶段激进策略的创新整合，并辅以比较器感知的混合策略。据我们所知，这提供了全信息设定下首个"三世界最优"保证，证实了基准安全性无需以牺牲最坏情况鲁棒性或随机效率为代价。