Bayesian Experimental Design via Contrastive Diffusions

TL;DR

This paper introduces a novel Bayesian experimental design method that leverages diffusion models and a pooled posterior distribution to efficiently optimize expected information gain, enabling practical high-dimensional experimental planning.

Contribution

It presents a new EIG gradient expression and a joint sampling-optimization approach using diffusion models, extending BOED to complex, high-dimensional problems.

Findings

Demonstrates improved efficiency over existing methods

Enables application of BOED with generative diffusion models

Shows promising results in numerical experiments

Abstract

Bayesian Optimal Experimental Design (BOED) is a powerful tool to reduce the cost of running a sequence of experiments. When based on the Expected Information Gain (EIG), design optimization corresponds to the maximization of some intractable expected contrast between prior and posterior distributions. Scaling this maximization to high dimensional and complex settings has been an issue due to BOED inherent computational complexity. In this work, we introduce a pooled posterior distribution with cost-effective sampling properties and provide a tractable access to the EIG contrast maximization via a new EIG gradient expression. Diffusion-based samplers are used to compute the dynamics of the pooled posterior and ideas from bi-level optimization are leveraged to derive an efficient joint sampling-optimization loop. The resulting efficiency gain allows to extend BOED to the well-tested generative capabilities of diffusion models. By incorporating generative models into the BOED framework, we expand its scope and its use in scenarios that were previously impractical. Numerical experiments and comparison with state-of-the-art methods show the potential of the approach.