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

2026-04-05

AI Summary

This work addresses the sensitivity of nonlinear Bayesian optimal experimental design to utility fluctuations and its insufficient robustness by proposing a mean–variance risk-aware optimization framework. The approach introduces a variance penalty term into the expected utility, yielding an objective function that balances performance and stability. To the best of our knowledge, this is the first integration of mean–variance risk measures into Bayesian experimental design. The method employs prior-based Monte Carlo estimation and derives an analytical expression for utility variance via the conditional Delta method, while leveraging common random seeds within a Bayesian optimization scheme to circumvent explicit posterior sampling. Experimental results demonstrate that the proposed framework substantially reduces the variability of design utility while maintaining competitive expected utility.

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.

Problem

• Bayesian optimal experimental design
• mean-variance
• risk-aware
• nonlinear models
• utility variability

Innovation

• mean-variance optimization
• Bayesian optimal experimental design
• variance-penalized utility
• Monte Carlo estimation
• nonlinear models