Gradient-Free Sequential Bayesian Experimental Design via Interacting Particle Systems

• URL: http://arxiv.org/abs/2504.13320v1
• Date: Thu, 17 Apr 2025 20:16:15 GMT
• Title: Gradient-Free Sequential Bayesian Experimental Design via Interacting Particle Systems
• Authors: Robert Gruhlke, Matei Hanu, Claudia Schillings, Philipp Wacker,
• Abstract summary: We introduce a gradient-free framework for Bayesian Optimal Experimental Design (BOED) in sequential settings.<n>Our method combines Ensemble Kalman Inversion (EKI) for design optimization with the Affine-Invariant Langevin Dynamics (ALDI) sampler for efficient posterior sampling.<n> variational Gaussian and parametrized Laplace approximations provide tractable upper and lower bounds on the Expected Information Gain.
• Score: 2.624902795082451
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We introduce a gradient-free framework for Bayesian Optimal Experimental Design (BOED) in sequential settings, aimed at complex systems where gradient information is unavailable. Our method combines Ensemble Kalman Inversion (EKI) for design optimization with the Affine-Invariant Langevin Dynamics (ALDI) sampler for efficient posterior sampling-both of which are derivative-free and ensemble-based. To address the computational challenges posed by nested expectations in BOED, we propose variational Gaussian and parametrized Laplace approximations that provide tractable upper and lower bounds on the Expected Information Gain (EIG). These approximations enable scalable utility estimation in high-dimensional spaces and PDE-constrained inverse problems. We demonstrate the performance of our framework through numerical experiments ranging from linear Gaussian models to PDE-based inference tasks, highlighting the method's robustness, accuracy, and efficiency in information-driven experimental design.

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