Optimal Design via Curve Fitting of Monte Carlo Experiments
Abstract This article explores numerical methods for stochastic optimization, with special attention to Bayesian design problems. A common and challenging situation occurs when the objective function (in Bayesian applications, the expected utility) is very expensive to evaluate, perhaps because it requires integration over a space of very large dimensionality. Our goal is to explore a class of optimization algorithms designed to gain efficiency in such situations, by exploiting smoothness of the expected utility surface and borrowing information from neighboring design points. The central idea is that of implementing stochastic optimization by curve fitting of Monte Carlo samples. This is done by simulating draws from the joint parameter/sample space and evaluating the observed utilities. Fitting a smooth surface through these simulated points serves as estimate for the expected utility surface. The optimal design can then be found deterministically. In this article we introduce a general algorithm for cu...