Score Matching Decouples Double Intractability to Speed Up Bayesian Design

Policy-based Bayesian experimental design (BED) uses deep networks to adaptively choose experiments based on previous data—but training these policies has been held back by the double intractability of the EIG. Traditional methods require expensive or complex approximations, limiting how much effort can be invested in optimizing the policy itself. In their paper accepted at UAI 2026, Phillips, Kerrigan, and Rainforth show that the double intractability can be isolated from policy learning by first solving a score matching problem that is independent of the policy. This pre-learned score approximation makes the subsequent policy training only singly intractable, converting a multiplicative cost into an additive one and removing the need to recompute likelihoods iteratively.

Crucially, this additive cost structure makes it far cheaper to train the policy multiple times—a necessity for architecture search, hyperparameter tuning, or escaping local optima. The authors demonstrate training multiple competitive policies without incurring multiplicative likelihood evaluation costs, achieving better performance simply by being able to train and select the best policy more efficiently. For practitioners, this means faster iteration when designing adaptive experiments in fields like clinical trials, A/B testing, and robotics, without the prohibitive computational overhead that previously constrained BED at scale.