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.

翻译：在Bayesian实验设计中,按预期获得的信息进行实验的排序对模型先前分布的变化十分敏感,而通过抽样得出的EIG近似于使用过敏的先前信息获取值的差错。我们定义和分析了\emph{robust预期信息获取值(REIG),通过尽可能减少EIG对接近于KL-diverence原先的模棱两可分布图的模棱两可度,修改了EIG最大化目标。我们表明,在与基于抽样估计EIG的方法相结合的情况下,REIG与用于估计EIG的样品的“总和”稳定性相对应,这意味着在实际中可以有效地实施。将REIG与变形的蒙特卡洛(VNMC)、适应性对比估计(ACE)和相互信息神经估计(MINE)相结合的数值试验表明,在实践中,REIG还补偿了抽样不足的估测者的变异性。