Thresholding Bandit for Dose-ranging: The Impact of Monotonicity
This work addresses the problem of dose-ranging in phase 1 clinical trials, where monotonicity is inherent, offering a solution where none existed before, though it is incremental in improving sample complexity analysis.
The paper tackles the thresholding bandit problem in dose-ranging, analyzing sample complexity with and without monotonicity assumptions, and provides lower bounds and an algorithm with matching order for small risks, achieving results in a practically important clinical trial setting.
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 $δ$ and any $δ$-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.