Regret Minimization in Heavy-Tailed Bandits

• URL: http://arxiv.org/abs/2102.03734v1
• Date: Sun, 7 Feb 2021 07:46:24 GMT
• Title: Regret Minimization in Heavy-Tailed Bandits
• Authors: Shubhada Agrawal, Sandeep Juneja, Wouter M. Koolen
• Abstract summary: We revisit the classic regret-minimization problem in the multi-armed bandit setting. We propose an optimal algorithm that matches the lower bound exactly in the first-order term. We show that our index concentrates faster than the well known truncated or trimmed empirical mean estimators.
• Score: 12.272975892517039
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We revisit the classic regret-minimization problem in the stochastic multi-armed bandit setting when the arm-distributions are allowed to be heavy-tailed. Regret minimization has been well studied in simpler settings of either bounded support reward distributions or distributions that belong to a single parameter exponential family. We work under the much weaker assumption that the moments of order $(1+\epsilon)$ are uniformly bounded by a known constant B, for some given $\epsilon > 0$. We propose an optimal algorithm that matches the lower bound exactly in the first-order term. We also give a finite-time bound on its regret. We show that our index concentrates faster than the well known truncated or trimmed empirical mean estimators for the mean of heavy-tailed distributions. Computing our index can be computationally demanding. To address this, we develop a batch-based algorithm that is optimal up to a multiplicative constant depending on the batch size. We hence provide a controlled trade-off between statistical optimality and computational cost.

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