  We study the problem of finding the optimal dosage in early stage clinical
trials through the multi-armed bandit lens. We advocate the use of the Thompson
Sampling principle, a flexible algorithm that can accommodate different types
of monotonicity assumptions on the toxicity and efficacy of the doses. For the
simplest version of Thompson Sampling, based on a uniform prior distribution
for each dose, we provide finite-time upper bounds on the number of sub-optimal
dose selections, which is unprecedented for dose-finding algorithms. Through a
large simulation study, we then show that variants of Thompson Sampling based
on more sophisticated prior distributions outperform state-of-the-art dose
identification algorithms in different types of dose-finding studies that occur
in phase I or phase I/II trials.
