Bayesian Experimental Design via Score Matching

Bayesian Experimental Design (BED) aims to select experimental designs that maximize the expected information gain (EIG) about target parameters. Policy-based approaches, which use deep neural networks to propose designs in real-time, are often hindered by the double intractability of the EIG. This requires expensive nested sampling or complex variational approximations, making the training of these policies computationally prohibitive.

The authors observe that the information gain itself depends on the observed data, not the policy used to collect it. They derive a reparameterized EIG gradient expression that isolates the double intractability into two terms: the Stein score and the Fisher score of the marginal likelihood. By training a single, policy-independent neural network to approximate these scores via a regression objective called Marginal Score Matching (MSM), the authors transform the doubly intractable EIG objective into a singly intractable one. This allows for gradient-based policy training without the need for nested sampling.

SCOREBED effectively separates the computational burden of approximating the EIG from the policy training process. Because the score network is learned upfront and is independent of the policy, it can be reused across multiple training runs. This allows researchers to perform cheaper hyperparameter tuning, architecture searches, and multiple restarts to avoid local optima. Experimental results demonstrate that SCOREBED achieves competitive performance compared to existing methods while significantly reducing the computational cost of policy optimization.

This approach provides a scalable solution for complex BED problems where likelihood evaluations are expensive. By turning a multiplicative cost into an additive one, SCOREBED makes it feasible to train more sophisticated policy architectures, which is essential for real-time experimental design in high-dimensional or computationally demanding scientific fields.