Supercharging Simulation-Based Inference for Bayesian Optimal Experimental Design
This work addresses the challenge of optimizing experiments in Bayesian settings for researchers in fields like statistics and machine learning, though it is incremental as it builds on existing SBI techniques.
The paper tackled the problem of Bayesian optimal experimental design (BOED) by leveraging simulation-based inference (SBI) to handle intractable likelihoods, resulting in methods that match or outperform existing state-of-the-art approaches by up to 22% on benchmarks.
Bayesian optimal experimental design (BOED) seeks to maximize the expected information gain (EIG) of experiments. This requires a likelihood estimate, which in many settings is intractable. Simulation-based inference (SBI) provides powerful tools for this regime. However, existing work explicitly connecting SBI and BOED is restricted to a single contrastive EIG bound. We show that the EIG admits multiple formulations which can directly leverage modern SBI density estimators, encompassing neural posterior, likelihood, and ratio estimation. Building on this perspective, we define a novel EIG estimator using neural likelihood estimation. Further, we identify optimization as a key bottleneck of gradient based EIG maximization and show that a simple multi-start parallel gradient ascent procedure can substantially improve reliability and performance. With these innovations, our SBI-based BOED methods are able to match or outperform by up to $22\%$ existing state-of-the-art approaches across standard BOED benchmarks.