  Bayesian optimal experimental design is a sub-field of statistics focused on
developing methods to make efficient use of experimental resources. Any
potential design is evaluated in terms of a utility function, such as the
(theoretically well-justified) expected information gain (EIG); unfortunately
however, under most circumstances the EIG is intractable to evaluate. In this
work we build off of successful variational approaches, which optimize a
parameterized variational model with respect to bounds on the EIG. Past work
focused on learning a new variational model from scratch for each new design
considered. Here we present a novel neural architecture that allows
experimenters to optimize a single variational model that can estimate the EIG
for potentially infinitely many designs. To further improve computational
efficiency, we also propose to train the variational model on a significantly
cheaper-to-evaluate lower bound, and show empirically that the resulting model
provides an excellent guide for more accurate, but expensive to evaluate bounds
on the EIG. We demonstrate the effectiveness of our technique on generalized
linear models, a class of statistical models that is widely used in the
analysis of controlled experiments. Experiments show that our method is able to
greatly improve accuracy over existing approximation strategies, and achieve
these results with far better sample efficiency.
