Robust Expected Information Gain for Optimal Bayesian Experimental Design Using Ambiguity Sets
This work addresses robustness issues in Bayesian experimental design for researchers and practitioners, but it is incremental as it modifies an existing objective rather than introducing a new paradigm.
The paper tackles the sensitivity of expected information gain (EIG) to prior distribution changes in Bayesian experimental design by introducing robust expected information gain (REIG), which minimizes an affine relaxation over an ambiguity set, and shows that REIG can be efficiently implemented via log-sum-exp stabilization and improves performance in numerical tests with methods like VNMC, ACE, and MINE.
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.