Batch-based Bayesian Optimal Experimental Design in Linear Inverse Problems

2026-02-12

AI Summary

This study addresses the non-convex optimization challenge in multivariate batch experimental design over continuous domains, focusing on A-optimal design under linear Bayesian inverse problems. The authors relax the original problem into the space of finite positive measures and, for the first time, rigorously establish a correspondence between this relaxed formulation and Bayesian inference. Building on this foundation, they propose an optimization framework integrating Wasserstein gradient flows along with a novel regularization strategy that guarantees convergence to an empirical measure. Theoretical analysis confirms the convergence properties of the proposed method, while numerical experiments demonstrate that the new regularization mechanism significantly enhances both the stability and effectiveness of the optimization process.

Technology Category

• Search and Optimization: Non-convex Optimization
• Machine Learning: Optimization
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

Experimental design is central to science and engineering. A ubiquitous challenge is how to maximize the value of information obtained from expensive or constrained experimental settings. Bayesian optimal experimental design (OED) provides a principled framework for addressing such questions. In this paper, we study experimental design problems such as the optimization of sensor locations over a continuous domain in the context of linear Bayesian inverse problems. We focus in particular on batch design, that is, the simultaneous optimization of multiple design variables, which leads to a notoriously difficult non-convex optimization problem. We tackle this challenge using a promising strategy recently proposed in the frequentist setting, which relaxes A-optimal design to the space of finite positive measures. Our main contribution is the rigorous identification of the Bayesian inference problem corresponding to this relaxed A-optimal OED formulation. Moreover, building on recent work, we develop a Wasserstein gradient-flow -based optimization algorithm for the expected utility and introduce novel regularization schemes that guarantee convergence to an empirical measure. These theoretical results are supported by numerical experiments demonstrating both convergence and the effectiveness of the proposed regularization strategy.

Problem

• Bayesian optimal experimental design
• batch design
• linear inverse problems
• sensor placement
• non-convex optimization

Innovation

• Bayesian optimal experimental design
• batch design
• Wasserstein gradient flow
• A-optimal design
• regularization