Bayesian Experimental Design (BED), which aims to find the optimal experimental conditions for Bayesian inference, is usually posed as to optimize the expected information gain (EIG). The gradient information is often needed for efficient EIG optimization, and as a result the ability to estimate the gradient of EIG is essential for BED problems. The primary goal of this work is to develop methods for estimating the gradient of EIG, which, combined with the stochastic gradient descent algorithms, result in efficient optimization of EIG. Specifically, we first introduce a posterior expected representation of the EIG gradient with respect to the design variables. Based on this, we propose two methods for estimating the EIG gradient, UEEG-MCMC that leverages posterior samples generated through Markov Chain Monte Carlo (MCMC) to estimate the EIG gradient, and BEEG-AP that focuses on achieving high simulation efficiency by repeatedly using parameter samples. Theoretical analysis and numerical studies illustrate that UEEG-MCMC is robust agains the actual EIG value, while BEEG-AP is more efficient when the EIG value to be optimized is small. Moreover, both methods show superior performance compared to several popular benchmarks in our numerical experiments.

翻译：贝叶斯实验设计（BED）旨在寻找贝叶斯推断的最优实验条件，通常表述为优化期望信息增益（EIG）。高效的EIG优化常需梯度信息，因此估计EIG梯度的能力对BED问题至关重要。本研究的主要目标是开发估计EIG梯度的方法，这些方法与随机梯度下降算法相结合，可实现EIG的高效优化。具体而言，我们首先引入关于设计变量的EIG梯度的后验期望表示。基于此，我们提出两种EIG梯度估计方法：UEEG-MCMC利用通过马尔可夫链蒙特卡洛（MCMC）生成的后验样本估计EIG梯度，而BEEG-AP则通过重复使用参数样本实现高仿真效率。理论分析与数值研究表明，UEEG-MCMC对实际EIG值具有稳健性，而BEEG-AP在待优化的EIG值较小时更为高效。此外，在我们的数值实验中，两种方法均优于若干主流基准方法。