Almost Optimal Algorithms for Linear Stochastic Bandits with Heavy-Tailed Payoffs
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AbstractIn linear stochastic bandits, it is commonly assumed that payoffs are with sub-Gaussian noises. In this paper, under a weaker assumption on noises, we study the problem of \underline{lin}ear stochastic {\underline b}andits with h{\underline e}avy-{\underline t}ailed payoffs (LinBET), where the distributions have finite moments of order 1+ϵ, for some ϵ∈(0,1]. We rigorously analyze the regret lower bound of LinBET as Ω(T11+ϵ), implying that finite moments of order 2 (i.e., finite variances) yield the bound of Ω(T‾‾√), with T being the total number of rounds to play bandits. The provided lower bound also indicates that the state-of-the-art algorithms for LinBET are far from optimal. By adopting median of means with a well-designed allocation of decisions and truncation based on historical information, we develop two novel bandit algorithms, where the regret upper bounds match the lower bound up to polylogarithmic factors. To the best of our knowledge, we are the first to solve LinBET optimally in the sense of the polynomial order on T. Our proposed algorithms are evaluated based on synthetic datasets, and outperform the state-of-the-art results.
All Author(s) ListHan Shao, Xiaotian Yu, Irwin King, Michael R. Lyu
Name of Conference32nd Conference on Neural Information Processing Systems (NIPS)
Start Date of Conference02/12/2018
End Date of Conference08/12/2018
Place of ConferenceMontreal, Canada
Country/Region of ConferenceCanada
Proceedings TitleAdvances in Neural Information Processing Systems 31 (NIPS 2018)
LanguagesEnglish-United States

Last updated on 2020-21-01 at 01:33