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Thresholding Bandit for Dose-ranging: The Impact of Monotonicity (1711.04454v2)
Published 13 Nov 2017 in math.ST, stat.ML, and stat.TH
Abstract: We analyze the sample complexity of the thresholding bandit problem, with and without the assumption that the mean values of the arms are increasing. In each case, we provide a lower bound valid for any risk $\delta$ and any $\delta$-correct algorithm; in addition, we propose an algorithm whose sample complexity is of the same order of magnitude for small risks. This work is motivated by phase 1 clinical trials, a practically important setting where the arm means are increasing by nature, and where no satisfactory solution is available so far.