Distributional Bayesian Optimal Experimental Design

Sequential Bayesian optimal experimental design (BOED) chooses informative experiments adaptively based on the outcomes of prior experiments. The standard sequential BOED objective, expected information gain (EIG), scores an experimental design policy by the mean of its information gain (IG) distribution. However, the mean alone can obscure important characteristics of the distribution, such as its variance or lower-tail behavior. To address this limitation, we present DistBOED, a distributional learning method for sequential BOED that models the full distribution of IG induced by a design policy. DistBOED uses a quantile critic and a campaign-level actor update to learn policies for objectives beyond mean IG. We demonstrate DistBOED across three different scenarios with various risk-sensitive IG measures including: conditional value at risk, variance-penalized mean, and entropic risk measure. In each case we observe that accounting for higher-order aspects of the IG distribution yields more robust design policies than EIG alone.