A Simple and Optimal Policy Design with Safety against Heavy-Tailed Risk for Stochastic Bandits

We study the stochastic multi-armed bandit problem and design new policies that enjoy both worst-case optimality for expected regret and light-tailed risk for regret distribution. Specifically, our policy design (i) enjoys the worst-case optimality for the expected regret at order $O(\sqrt{KT\ln T})$ and (ii) has the worst-case tail probability of incurring a regret larger than any $x>0$ being…