Response adaptive designs that incorporate switching costs and constraints

Abstract

This paper examines the design and performance of sequential experiments where extensive switching is undesirable. Given an objective function to optimize by sampling between Bernoulli populations, two different models are considered. The constraint model restricts the maximum number of switches possible, while the cost model introduces a charge for each switch. Optimal allocation procedures and a new "hyperopic" procedure are discussed and their behavior examined. For the cost model, if one views the costs as control variables then the optimal allocation procedures yield the optimal tradeoff of expected switches vs. expected value of the objective function.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 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.