An Adaptive Algorithm based on High-Dimensional Function Approximation to obtain Optimal Designs

Abstract

Algorithms which compute locally optimal continuous designs often rely on a finite design space or on repeatedly solving a complex non-linear program. Both methods require extensive evaluations of the Jacobian Df of the underlying model. These evaluations present a heavy computational burden. Based on the Kiefer-Wolfowitz Equivalence Theorem we present a novel design of experiments algorithm which computes optimal designs in a continuous design space. For this iterative algorithm we combine an adaptive Bayes-like sampling scheme with Gaussian process regression to approximate the directional derivative of the design criterion. The approximation allows us to adaptively select new design points on which to evaluate the model. The adaptive selection of the algorithm requires significantly less evaluations of Df and reduces the runtime of the computations. We show the viability of the new algorithm on two examples from chemical engineering.