Bayesian Experimental Design via Score Matching

Angus Phillips, Gavin Kerrigan, Tom Rainforth
Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence, PMLR 337:5393-5426, 2026.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v337-phillips26a, title = {{Bayesian} Experimental Design via Score Matching}, author = {Phillips, Angus and Kerrigan, Gavin and Rainforth, Tom}, booktitle = {Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence}, pages = {5393--5426}, year = {2026}, editor = {Perković, Emilija and Malinsky, Daniel}, volume = {337}, series = {Proceedings of Machine Learning Research}, month = {17--21 Aug}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v337/main/assets/phillips26a/phillips26a.pdf}, url = {https://proceedings.mlr.press/v337/phillips26a.html}, 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.} }
Endnote
%0 Conference Paper %T Bayesian Experimental Design via Score Matching %A Angus Phillips %A Gavin Kerrigan %A Tom Rainforth %B Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2026 %E Emilija Perković %E Daniel Malinsky %F pmlr-v337-phillips26a %I PMLR %P 5393--5426 %U https://proceedings.mlr.press/v337/phillips26a.html %V 337 %X 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.
APA
Phillips, A., Kerrigan, G. & Rainforth, T.. (2026). Bayesian Experimental Design via Score Matching. Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research 337:5393-5426 Available from https://proceedings.mlr.press/v337/phillips26a.html.

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