Robust Expected Information Gain for Optimal Bayesian Experimental Design Using Ambiguity Sets

TL;DR

This paper introduces Robust Expected Information Gain (REIG), a method that stabilizes Bayesian experimental design against prior distribution uncertainties by minimizing over an ambiguity set, improving the reliability of experiment ranking.

Contribution

The paper proposes REIG, a novel approach that enhances Bayesian experimental design by incorporating ambiguity sets and stabilization techniques for more robust experiment ranking.

Findings

REIG stabilizes EIG estimates with a log-sum-exp approach.

Numerical tests show REIG compensates for estimator variability.

REIG improves robustness against prior distribution perturbations.

Abstract

The ranking of experiments by expected information gain (EIG) in Bayesian experimental design is sensitive to changes in the model's prior distribution, and the approximation of EIG yielded by sampling will have errors similar to the use of a perturbed prior. We define and analyze \emph{robust expected information gain} (REIG), a modification of the objective in EIG maximization by minimizing an affine relaxation of EIG over an ambiguity set of distributions that are close to the original prior in KL-divergence. We show that, when combined with a sampling-based approach to estimating EIG, REIG corresponds to a `log-sum-exp' stabilization of the samples used to estimate EIG, meaning that it can be efficiently implemented in practice. Numerical tests combining REIG with variational nested Monte Carlo (VNMC), adaptive contrastive estimation (ACE) and mutual information neural estimation (MINE) suggest that in practice REIG also compensates for the variability of under-sampled estimators.