Bayesian Optimal Experimental Design (BOED) provides a rigorous framework for decision-making tasks in which data acquisition is often the critical bottleneck, especially in resource-constrained settings. Traditionally, BOED typically selects designs by maximizing expected information gain (EIG), commonly defined through the Kullback-Leibler (KL) divergence. However, classical evaluation of EIG often involves challenging nested expectations, and even advanced variational methods leave the underlying log-density-ratio objective unchanged. As a result, support mismatch, tail underestimation, and rare-event sensitivity remain intrinsic concerns for KL-based BOED. To address these fundamental bottlenecks, we introduce an IPM-based BOED framework that replaces density-based divergences with integral probability metrics (IPMs), including the Wasserstein distance, Maximum Mean Discrepancy, and Energy Distance, resulting in a highly flexible plug-and-play BOED framework. We establish theoretical guarantees showing that IPM-based utilities provide stronger geometry-aware stability under surrogate-model error and prior misspecification than classical EIG-based utilities. We also validate the proposed framework empirically, demonstrating that IPM-based designs yield highly concentrated credible sets. Furthermore, by extending the same sample-based BOED template in a plug-and-play manner to geometry-aware discrepancies beyond the IPM class, illustrated by a neural optimal transport estimator, we achieve accurate optimal designs in high-dimensional settings where conventional nested Monte Carlo estimators and advanced variational methods fail.

翻译：贝叶斯最优实验设计（BOED）为数据获取常成为关键瓶颈的决策任务提供了严谨框架，尤其适用于资源受限场景。传统BOED通常通过最大化基于Kullback-Leibler（KL）散度定义的期望信息增益（EIG）来选取设计。然而，经典EIG评估常涉及复杂的嵌套期望，即便是先进的变分方法也未能改变其底层对数密度比目标函数。因此，支撑域失配、尾部低估及罕见事件敏感性始终是基于KL散度的BOED的固有难题。为解决这些根本性瓶颈，我们提出基于积分概率度量（IPM）的BOED框架，将基于密度的散度替换为Wasserstein距离、最大均值差异和能量距离等IPM，从而构建高度灵活的即插即用型BOED框架。我们建立了理论保证，表明在替代模型误差与先验设定错误下，基于IPM的效用函数相较于经典EIG效用函数具有更强的几何感知稳定性。通过实验验证，基于IPM的设计能产生高度集中的可信集。此外，通过将同一基于样本的BOED模板以即插即用方式扩展到IPM类之外的几何感知差异度量（以神经最优传输估计器为例），我们在传统嵌套蒙特卡洛估计器与先进变分方法失效的高维场景中实现了精确的最优设计。