Chapter 1 OPTIMIZING A UNIMODAL RESPONSEFUNCTION FOR BINARY VARIABLESJanis

Several allocation rules are examined for the problem of optimizing a response function for a set of Bernoulli populations, where the population means are assumed to have a strict unimodal structure. This problem arises in dose response settings in clinical trials. The designs are evaluated both on their eeciency in identifying a good population at the end of the experiment, and in their eeciency in sampling from good populations during the trial. A new design, that adapts multi-arm bandit strategies to this unimodal structure, is shown to be superior to the designs previously proposed. The bandit design utilizes approximate Gittin's indices and shape constrained regression.