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）旨在为贝叶斯推断寻找最优实验条件，通常表述为优化期望信息增益（EIG）。高效优化EIG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，结合随机梯度下降算法实现EIG的高效优化。具体而言，我们首先引入EIG梯度关于设计变量的后验期望表示，并据此提出两种EIG梯度估计方法：UEEG-MCMC利用马尔可夫链蒙特卡洛（MCMC）生成的后验样本估计EIG梯度，BEEG-AP通过重复使用参数样本实现高仿真效率。理论分析和数值研究表明，UEEG-MCMC对实际EIG值具有鲁棒性，而BEEG-AP在待优化EIG值较小时效率更高。此外，在数值实验中，两种方法相较于多个主流基准方法均表现出更优性能。