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

Jinwoo Go, Tobin Isaac

Keywords: Bayesian Experimental Design, Ambiguity set, Robustness, Uncertainty Quantification, Convex optimization, Risk averse, Bayesian Inference

TL;DR: We implement a robust variant of expected information gain (minimized in a small KL-divergence neighborhood) as a simple post-processing of existing estimators and test it on standard benchmarks in Bayesian experimental design.

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.