Bayesian optimal experimental design (BOED) seeks to maximize the expected information gain (EIG) of experiments. This requires a likelihood estimate, which in many settings is intractable. Simulation-based inference (SBI) provides powerful tools for this regime. However, existing work explicitly connecting SBI and BOED is restricted to a single contrastive EIG bound. We show that the EIG admits multiple formulations which can directly leverage modern SBI density estimators, encompassing neural posterior, likelihood, and ratio estimation. Building on this perspective, we define a novel EIG estimator using neural likelihood estimation. Further, we identify optimization as a key bottleneck of gradient based EIG maximization and show that a simple multi-start parallel gradient ascent procedure can substantially improve reliability and performance. With these innovations, our SBI-based BOED methods are able to match or outperform by up to $22\%$ existing state-of-the-art approaches across standard BOED benchmarks.

翻译：贝叶斯最优实验设计旨在最大化实验的期望信息增益。这需要似然估计，而在许多场景中该估计难以获得。基于仿真的推理为此类问题提供了强大的工具。然而，现有将SBI与BOED明确关联的研究仅限于单一的对比性EIG边界。我们证明EIG存在多种表述形式，可直接利用现代SBI密度估计器，涵盖神经后验估计、似然估计与比率估计。基于这一视角，我们利用神经似然估计定义了一种新颖的EIG估计器。此外，我们指出优化是基于梯度的EIG最大化的关键瓶颈，并证明简单的多起点并行梯度上升程序能显著提升可靠性与性能。凭借这些创新，我们基于SBI的BOED方法在标准BOED基准测试中能够匹配或超越现有最优方法，最高提升幅度达$22\%$。