Bayesian Experimental Design Via Contrastive Diffusions
Jacopo Iollo Christophe Heinkelé Pierre Alliez Florence Forbes
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 an *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, without resorting to lower bound approximations of the EIG. 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.
Bayesian Optimal Experimental Design, Conditional Diffusion Models, score based sampling, Bayesian Inverse Problems, Experimental Design, Sampling as Optimization
The paper introduces an efficient BOED method leveraging diffusion-based samplers and bi-level optimization ideas to jointly sample the introduced pooled posterior and maximize Expected Information Gain, enabling larger-scale applications.