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

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