Cover meets Robbins while Betting on Bounded Data: $\ln n$ Regret and Almost Sure $\ln\ln n$ Regret
Researchers have developed a new mixture betting strategy that combines elements of Robbins and Cover's work to achieve adaptive regret bounds. This novel approach demonstrates an $O(\ln \ln n)$ regret on almost all data paths, offering improved performance compared to existing methods. The strategy also provides protection against adversarial data, achieving a best-of-both-worlds adaptivity. This work contrasts with previous findings on sub-Gaussian mixtures, highlighting the benefits of hedging different strategies for optimal performance. AI
IMPACT Introduces a novel betting strategy with improved regret bounds for adaptive and adversarial data scenarios.