Response adaptive designs that incorporate switching costs and constraints

Our approach is quite general, applying to any objective function, and gives users flexibility in incorporating practical considerations in the design of experiments. To illustrate the effects of the switching restrictions, they are applied to the problems of minimizing failures and of minimizing the Bayes risk in a nonlinear estimation problem. It is observed that when there are no restrictions the expected number of switches in the optimal allocation grows approximately as the square root of the sample size, for sample sizes up to a few hundred. It is also observed that one can dramatically reduce the number of switches without substantially affecting the expected value of the objective function. The adaptive hyperopic procedure is introduced and it is seen to perform nearly as well as the optimal procedure. Thus, one need to sacrifice only a small amount of statistical objective in order to achieve significant gains in practicality. We also examine scenarios in which switching is desirable, even beyond that which would occur in the optimal design, and show that similar computational approaches can be applied.