Adaptive multiple-arm identification

Jiecao Chen, Xi Chen, Qin Zhang, Yuan Zhou

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We study the problem of selecting K arms with the highest expected rewards in a stochastic n-armed bandit game. This problem has a wide range of applications, e.g., A/B testing, crowd-sourcing, simulation optimization. Our goal is to develop a PAC algorithm, which, with probability at least 1 - δ, identifies a set of K arms with the aggregate regret at most e. The notion of aggregate regret for multiple-arm identification was first introduced in Zhou et al. (2014), which is defined as the difference of the averaged expected rewards between the selected set of arms and the best K arms. In contrast to Zhou et al. (2014) that only provides instance-independent sample complexity, we introduce a new hardness parameter for characterizing the difficulty of any given instance. We further develop two algorithms and establish the corresponding sample complexity in terms of this hardness parameter. The derived sample complexity can be significantly smaller than state-of-the-art results for a large class of instances and matches the instance-independent lower bound upto a log(e-1) factor in the worst case. We also prove a lower bound result showing that the extra log(ϵ-1) is necessary for instance-dependent algorithms using the introduced hardness parameter.

Original languageEnglish (US)
Title of host publication34th International Conference on Machine Learning, ICML 2017
PublisherInternational Machine Learning Society (IMLS)
Pages1202-1210
Number of pages9
ISBN (Electronic)9781510855144
StatePublished - Jan 1 2017
Externally publishedYes
Event34th International Conference on Machine Learning, ICML 2017 - Sydney, Australia
Duration: Aug 6 2017Aug 11 2017

Publication series

Name34th International Conference on Machine Learning, ICML 2017
Volume2

Other

Other34th International Conference on Machine Learning, ICML 2017
CountryAustralia
CitySydney
Period8/6/178/11/17

ASJC Scopus subject areas

  • Computational Theory and Mathematics
  • Human-Computer Interaction
  • Software

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