This paper studies the problem of adaptively sampling from K distributions (arms) in order to identify the largest gap between any two adjacent means. We call this the MaxGap-bandit problem. This problem arises naturally in approximate ranking, noisy sorting, outlier detection, and top-arm identification in bandits. The key novelty of the MaxGap bandit problem is that it aims to adaptively determine the natural partitioning of the distributions into a subset with larger means and a subset with smaller means, where the split is determined by the largest gap rather than a pre-specified rank or threshold. Estimating an arm's gap requires sampling its neighboring arms in addition to itself, and this dependence results in a novel hardness parameter that characterizes the sample complexity of the problem. We propose elimination and UCB-style algorithms and show that they are minimax optimal. Our experiments show that the UCB-style algorithms require 6-8x fewer samples than non-adaptive sampling to achieve the same error.

Meeting Name

33rd Conference on Neural Information Processing Systems, NeurIPS 2019 (2019: Dec. 8-14, Vancouver, Canada)


Computer Science


This work was partially supported by AFOSR/AFRL grants FA8750-17-2-0262 and FA9550-18-1-0166.

International Standard Serial Number (ISSN)


Document Type

Article - Conference proceedings

Document Version

Final Version

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© 2019 Neural Information Processing Systems Foundation, All rights reserved.

Publication Date

14 Dec 2019