Stochastic Gradient Bayesian Optimal Experimental Designs for Simulation-based Inference

TL;DR

This paper introduces a novel method that combines Bayesian optimal experimental design with simulation-based inference by connecting ratio-based SBI algorithms to stochastic gradient variational inference, enabling efficient experimental design in complex, non-differentiable models.

Contribution

The work establishes a key link between SBI inference algorithms and stochastic gradient variational inference, extending BOED to SBI applications.

Findings

Successfully applied to a simple linear model

Enables simultaneous optimization of experimental designs and inference functions

Provides implementation details for practical use

Abstract

Simulation-based inference (SBI) methods tackle complex scientific models with challenging inverse problems. However, SBI models often face a significant hurdle due to their non-differentiable nature, which hampers the use of gradient-based optimization techniques. Bayesian Optimal Experimental Design (BOED) is a powerful approach that aims to make the most efficient use of experimental resources for improved inferences. While stochastic gradient BOED methods have shown promising results in high-dimensional design problems, they have mostly neglected the integration of BOED with SBI due to the difficult non-differentiable property of many SBI simulators. In this work, we establish a crucial connection between ratio-based SBI inference algorithms and stochastic gradient-based variational inference by leveraging mutual information bounds. This connection allows us to extend BOED to SBI applications, enabling the simultaneous optimization of experimental designs and amortized inference functions. We demonstrate our approach on a simple linear model and offer implementation details for practitioners.