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