Mean--Variance Risk-Aware Bayesian Optimal Experimental Design for Nonlinear Models

TL;DR

This paper introduces a variance-penalized Bayesian experimental design method for nonlinear models, enhancing robustness by reducing utility variability through Monte Carlo estimators and Bayesian optimization.

Contribution

It develops a mean-variance objective for Bayesian design, with novel estimators and bias-variance analysis, improving design robustness in nonlinear modeling.

Findings

Designs with lower utility variability while maintaining expected utility.

Monte Carlo estimators avoid explicit posterior sampling.

Numerical examples show improved robustness in experimental design.

Abstract

We propose a variance-penalized formulation of Bayesian optimal experimental design for nonlinear models that augments the classical expected utility criterion with a penalty on utility variability, yielding a mean--variance objective that promotes robust experimental performance. To evaluate this objective, we develop Monte Carlo estimators for the expected utility, its second moment, and the resulting utility variance using prior sampling, thereby avoiding explicit posterior sampling. We then derive leading-order bias and variance expressions using conditional delta-method arguments. The objective is optimized using Bayesian optimization with common random samples to reduce noise. Numerical examples, including a linear-Gaussian benchmark, a nonlinear test problem, and contaminant source inversion in diffusion fields, demonstrate that the proposed approach identifies designs with substantially reduced variability while maintaining competitive expected utility.