Title: Thresholding Bandit for Dose-ranging: The Impact of Monotonicity,
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.