Bayesian Experimental Design via Score Matching

2026-07-09

AI Summary

This work addresses the high computational cost in Bayesian experimental design arising from the doubly intractable nature of expected information gain (EIG). The authors propose a decoupled approach that first learns the posterior score function independently via score matching and then leverages this learned score to construct a singly intractable approximation of EIG for policy optimization. By shifting the computational burden from multiplicative to additive, the method substantially reduces training costs without increasing the number of likelihood evaluations. This efficiency enables scalable training of multiple design policies and facilitates model selection, ultimately leading to improved performance of the final experimental design policy.

Abstract

Policy-based approaches to Bayesian experimental design (BED) allow the learning of deep policy networks that adaptively make intelligent design decisions based on previously collected data. However, the training of such policies is often held back by a fundamental challenge: the double intractability of the expected information gain (EIG). This necessitates expensive or complex approximations that restrict the effort one can invest in optimising the policy itself. To address this, we show that the double intractability of the EIG can be isolated from the policy learning by first solving a score matching problem that is independent of the policy used, then using the learned score approximation to train the policy in a singly intractable manner. This turns the key multiplicative cost into an additive one and reduces the computational burden on the policy training itself, making it far cheaper to train the policy multiple times when needed, e.g. for architecture search, hyperparameter tuning, or avoiding local optima. In our experiments we train multiple competitive policies without inducing a multiplicative cost in likelihood evaluations, which can increase performance by allowing us to select the best policy even without performing hyperparameter or architecture searches.

Problem

• Bayesian experimental design
• expected information gain
• double intractability
• policy learning
• score matching

Innovation

• Bayesian experimental design
• score matching
• expected information gain
• policy learning
• double intractability