Heavy-tailed distributions naturally arise in many settings, from finance to telecommunications. While regret minimization under sub-Gaussian or bounded support rewards has been widely studied, learning on heavy-tailed distributions only gained popularity over the last decade. In the stochastic heavy-tailed bandit problem, an agent learns under the assumption that the distributions have finite moments of maximum order $1+\epsilon$ which are uniformly bounded by a constant $u$, for some $\epsilon \in (0,1]$. To the best of our knowledge, literature only provides algorithms requiring these two quantities as an input. In this paper, we study the stochastic adaptive heavy-tailed bandit, a variation of the standard setting where both $\epsilon$ and $u$ are unknown to the agent. We show that adaptivity comes at a cost, introducing two lower bounds on the regret of any adaptive algorithm, implying a higher regret w.r.t. the standard setting. Finally, we introduce a specific distributional assumption and provide Adaptive Robust UCB, a regret minimization strategy matching the known lower bound for the heavy-tailed MAB problem.

学习重尾分布下的遗憾最小化问题，引入自适应算法并提供适应性鲁棒 UCB 方法，以最小化重尾 MAB 问题的遗憾。

重尾臂赌博机中实现全自适应遗憾最小化