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arxiv: 1711.04454 · v2 · pith:OQDDH55Fnew · submitted 2017-11-13 · 🧮 math.ST · stat.ML· stat.TH

Thresholding Bandit for Dose-ranging: The Impact of Monotonicity

Aur\'elien Garivier (IMT) , Pierre M\'enard (IMT) , Laurent Rossi (IMT) , Pierre Menard (IMT) This is my paper
classification 🧮 math.ST stat.MLstat.TH
keywords algorithmbanditcomplexitydeltaincreasingsamplethresholdingaddition
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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.

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