Tractable Global Solutions to Bayesian Optimal Experiment Design

Optimal experiment design (OED) aims to optimize the information content of experimental observations for various types of applications by designing the experimental conditions. In Bayesian OED for parameter estimation, the design selection is based on an expected utility metric that accounts for the joint probability distribution of the uncertain parameters and the observations. This work presents an approximation of the Bayesian OED problem based on Kullback-Leibler divergence that is amenable to global optimization. The experiment design adopts a parsimonious input parametrization that reduces the number of design variables. This leads to a tractable polynomial optimization problem that can be solved to global optimality via the concept of sum-of-squares polynomials.