# Gradient-Free Sequential Bayesian Experimental Design via Interacting Particle Systems

arXiv: https://arxiv.org/abs/2504.13320 · HTML: https://mlsanity.com/paper/2504.13320/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 59 references that are in the map.
- First posted on arXiv 17 Apr 2025.

## Builds on (most cited first, 14 of 14)

- [On Variational Bounds of Mutual Information](https://mlsanity.com/paper/1905.06922/) (2019)
- [Modern Bayesian Experimental Design](https://mlsanity.com/paper/2302.14545/) (2023)
- [Variational Bayesian Optimal Experimental Design](https://mlsanity.com/paper/1903.05480/) (2019)
- [Deep Adaptive Design: Amortizing Sequential Bayesian Experimental Design](https://mlsanity.com/paper/2103.02438/) (2021)
- [Optimal experimental design: Formulations and computations](https://mlsanity.com/paper/2407.16212/) (2024)
- [Sequential Bayesian optimal experimental design via approximate dynamic programming](https://mlsanity.com/paper/1604.08320/) (2016)
- [Analysis of Stochastic Gradient Descent in Continuous Time](https://mlsanity.com/paper/2004.07177/) (2020)
- [Tikhonov Regularization Within Ensemble Kalman Inversion](https://mlsanity.com/paper/1901.10382/) (2019)
- [Tractable Optimal Experimental Design using Transport Maps](https://mlsanity.com/paper/2401.07971/) (2024)
- [Ensemble Kalman Methods With Constraints](https://mlsanity.com/paper/1901.05668/) (2019)
- [Continuous Limits for Constrained Ensemble Kalman Filter](https://mlsanity.com/paper/1912.08406/) (2019)
- [Subspace accelerated measure transport methods for fast and scalable sequential experimental design, with application to photoacoustic imaging](https://mlsanity.com/paper/2502.20086/) (2025)
- [On the Incorporation of Box-Constraints for Ensemble Kalman Inversion](https://mlsanity.com/paper/1908.00696/) (2019)
- [Gradient flow structure and convergence analysis of the ensemble Kalman inversion for nonlinear forward models](https://mlsanity.com/paper/2203.17117/) (2022)

## Abstract (arXiv)

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.