A polynomial chaos efficient global optimization approach for Bayesian optimal experimental design

Abstract

This paper proposes a global optimization framework to address the high computational cost and non convexity of Optimal Experimental Design (OED) problems. To reduce the computational burden and the presence of noise in the evaluation of the Shannon expected information gain (SEIG), this framework proposes the coupling of Laplace approximation and polynomial chaos expansions (PCE). The advantage of this procedure is that PCE allows large samples to be employed for the SEIG estimation, practically vanishing the noisy introduced by the sampling procedure. Consequently, the resulting optimization problem may be treated as deterministic. Then, an optimization approach based on Kriging surrogates is employed as the optimization engine to search for the global solution with limited computational budget. Four numerical examples are investigated and their results are compared to state-of-the-art stochastic gradient descent algorithms. The proposed approach obtained better results than the stochastic gradient algorithms in all situations, indicating its efficiency and robustness in the solution of OED problems.