COMPASS-Hedge: Learning Safely Without Knowing the World
arXiv:2603.22348v1 Announce Type: new 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
arXiv:2603.22348v1 Announce Type: new 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.
Executive Summary
The article presents COMPASS-Hedge, a novel online learning algorithm that achieves minimax-optimal regret in adversarial environments, instance-optimal, gap-dependent regret in stochastic environments, and baseline safety against a fixed comparator. COMPASS-Hedge is parameter-free, adaptive, and requires no prior knowledge of the environment's nature or the magnitude of stochastic sub-optimality gaps. This work bridges the gap between existing methods that excel in one or two of these regimes and provides a unified solution without sacrificing optimal rates or requiring oracle access. The algorithm's integration of adaptive pseudo-regret scaling, phase-based aggression, and comparator-aware mixing strategy enables baseline safety without compromising worst-case robustness or stochastic efficiency.
Key Points
- ▸ COMPASS-Hedge achieves minimax-optimal regret in adversarial environments
- ▸ COMPASS-Hedge achieves instance-optimal, gap-dependent regret in stochastic environments
- ▸ COMPASS-Hedge provides baseline safety against a fixed comparator without sacrificing optimal rates
Merits
Comprehensive Solution
COMPASS-Hedge provides a unified solution for online learning, addressing the trilemma of balancing regret guarantees in adversarial and stochastic settings and providing baseline safety.
Adaptability
COMPASS-Hedge is parameter-free and adaptive, requiring no prior knowledge of the environment's nature or the magnitude of stochastic sub-optimality gaps.
Optimal Rates
COMPASS-Hedge achieves optimal rates without sacrificing baseline safety or worst-case robustness.
Demerits
Complexity
The algorithm's integration of adaptive pseudo-regret scaling, phase-based aggression, and comparator-aware mixing strategy may add complexity to the implementation.
Scalability
The performance of COMPASS-Hedge in large-scale environments remains to be explored.
Expert Commentary
The article presents a significant contribution to the field of online learning, providing a unified solution that addresses the trilemma of balancing regret guarantees in adversarial and stochastic settings and providing baseline safety. The authors' innovative approach, which integrates adaptive pseudo-regret scaling, phase-based aggression, and comparator-aware mixing strategy, demonstrates a deep understanding of the underlying challenges and opportunities. While the algorithm's complexity and scalability remain to be explored, the potential implications for real-world applications and policy development are substantial.
Recommendations
- ✓ Future research should focus on exploring the performance of COMPASS-Hedge in large-scale environments and evaluating its scalability.
- ✓ The development of COMPASS-Hedge highlights the need for more comprehensive solutions that address the trilemma of balancing regret guarantees in online learning, and researchers should continue to explore innovative approaches to address this challenge.
Sources
Original: arXiv - cs.LG
