Bayesian optimal experimental design (OED) seeks to conduct the most informative experiment under budget constraints to update the prior knowledge of a system to its posterior from the experimental data in a Bayesian framework. Such problems are computationally challenging because of (1) expensive and repeated evaluation of some optimality criterion that typically involves a double integration with respect to both the system parameters and the experimental data, (2) suffering from the curse-of-dimensionality when the system parameters and design variables are high-dimensional, (3) the optimization is combinatorial and highly non-convex if the design variables are binary, often leading to non-robust designs. To make the solution of the Bayesian OED problem efficient, scalable, and robust for practical applications, we propose a novel joint optimization approach. This approach performs simultaneous (1) training of a scalable conditional normalizing flow (CNF) to efficiently maximize the expected information gain (EIG) of a jointly learned experimental design (2) optimization of a probabilistic formulation of the binary experimental design with a Bernoulli distribution. We demonstrate the performance of our proposed method for a practical MRI data acquisition problem, one of the most challenging Bayesian OED problems that has high-dimensional (320 $\times$ 320) parameters at high image resolution, high-dimensional (640 $\times$ 386) observations, and binary mask designs to select the most informative observations.

翻译：贝叶斯最优实验设计（OED）旨在预算约束下进行最具信息量的实验，在贝叶斯框架中利用实验数据将系统的先验知识更新为后验知识。这类问题在计算上具有挑战性，原因在于：（1）对通常涉及系统参数与实验数据双重积分的最优性准则进行昂贵且重复的评估；（2）当系统参数和设计变量为高维时，面临维度灾难；（3）若设计变量为二元变量，优化问题具有组合性与高度非凸性，常导致非稳健的设计。为使贝叶斯OED问题在实际应用中实现高效、可扩展且稳健的求解，我们提出了一种新型联合优化方法。该方法同步执行：（1）训练可扩展的条件归一化流（CNF）以高效最大化联合学习实验设计的期望信息增益（EIG）；（2）利用伯努利分布对二元实验设计进行概率公式的优化。我们通过一个实际的MRI数据采集问题验证了所提方法的性能——该问题是贝叶斯OED中最具挑战性的问题之一，涉及高分辨率下高维（320 × 320）参数、高维（640 × 386）观测数据以及用于选择最具信息量观测的二元掩模设计。