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This paper addresses the challenge of double intractability in Bayesian experimental design (BED) by introducing a method that decouples the expected information gain (EIG) from policy learning. By solving a score matching problem independently of the policy, the authors transform the training process from a multiplicative to an additive cost, significantly reducing computational demands. Experimental results demonstrate that this approach enables the training of multiple competitive policies efficiently, enhancing performance without the need for extensive hyperparameter tuning or architecture searches.
By isolating the double intractability of expected information gain, this method slashes the computational costs of training adaptive policies in Bayesian experimental design.
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.
