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Indian Institute of Science, Tata Institute of Fundamental Research, Mumbai
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By cleverly hedging between Cover's and Robbins' betting strategies, you can achieve almost-sure $O(\ln \ln n)$ regret without sacrificing the $O(\ln n)$ worst-case guarantee.
Asymptotically optimal bandit algorithms can still exhibit heavy regret tails, but this work provides a unified and tight characterization of these tails for KL-based UCB algorithms even beyond parametric models.