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This paper introduces a Bayesian Optimal Experimental Design (BOED) framework that replaces the traditional Kullback-Leibler (KL) divergence with integral probability metrics (IPMs) like Wasserstein distance and Maximum Mean Discrepancy. By using IPMs, the framework overcomes limitations of KL-based BOED, such as sensitivity to support mismatch and tail underestimation. The authors demonstrate theoretically and empirically that IPM-based designs offer stronger stability under model error and prior misspecification, leading to more concentrated credible sets and accurate designs, especially in high-dimensional settings.
Ditch KL divergence for IPMs in Bayesian experimental design and watch your credible sets tighten and your designs stabilize, even when your model's a bit off.
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.
