Supercharging Simulation-Based Inference for Bayesian Optimal Experimental Design

2026-02-06

AI Summary

This work addresses the challenge in Bayesian optimal experimental design (BOED) where the intractability of the likelihood function hinders accurate estimation of the expected information gain (EIG). To overcome this, we propose a novel EIG estimator based on neural likelihood estimation, which integrates neural density estimation with a multi-start parallel gradient ascent strategy to enhance both the stability and efficiency of the optimization process. Our approach provides a unified framework that coherently combines neural posterior, likelihood, and ratio estimation—key techniques in simulation-based inference. Evaluated on standard BOED benchmarks, the proposed method matches or exceeds the performance of current state-of-the-art approaches, achieving improvements of up to 22%.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Machine Learning: Bayesian Learning
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Economics, Online Markets and Human Computation: Uses of LLMs and GenAI for marketplace design, bidding, and strategic interactions
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

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.

Problem

• Bayesian optimal experimental design
• expected information gain
• simulation-based inference
• intractable likelihood

Innovation

• simulation-based inference
• Bayesian optimal experimental design
• expected information gain
• neural likelihood estimation
• multi-start gradient ascent