From Bandits to Ethical Clinical Trials. Optimal Sample Size for Multi-Phases Problems.

In the first part of this talk, I will present recent results on the problem of sequential allocations called “multi-armed bandit”. Given several i.i.d. processes, the objective is to sample them sequentially (and thus get a sequence of random rewards) in order to maximize the expected cumulative reward. This framework simultaneously encompasses issues of estimation and optimization (the so-called “exploration vs exploitation” dilemma). A recent example of applications is the ad placement on web sites.
In the second part, I will come back to the original motivation of bandit problems: clinical trials. They usually consist of a small number of phases (typically three or four). The first phase is a pilot study and treatment can be allocated at random. In the following phases, treatments are re-allocated depending on the result of the pilot study (and the subsequent phases). We will show how to theoretically choose the sizes of these phases and we shall look whether having more phases leads to significant improvements.