Gradient-Free Sequential Bayesian Experimental Design via Interacting Particle Systems
This addresses computational challenges in experimental design for complex systems like PDE-constrained inverse problems, though it appears incremental as it builds on existing ensemble-based methods with new approximations.
The paper tackles the problem of Bayesian Optimal Experimental Design in sequential settings where gradient information is unavailable, by introducing a gradient-free framework that combines Ensemble Kalman Inversion and Affine-Invariant Langevin Dynamics with variational approximations for Expected Information Gain, demonstrating robustness, accuracy, and efficiency in numerical experiments including PDE-based inference tasks.
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.