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.

该研究提出了一种修改后的EIG最大化目标函数，称之为REIG，并利用其在近似KL-散度的先验概率分布的模糊区间内最小化关于EIG的仿射松弛。研究表明，当与基于采样的EIG估计相结合时，REIG对可估计量的变异性也进行了补偿。

使用不确定性集合的鲁棒期望信息增益优化贝叶斯实验设计