  We introduce a fully stochastic gradient based approach to Bayesian optimal
experimental design (BOED). Our approach utilizes variational lower bounds on
the expected information gain (EIG) of an experiment that can be simultaneously
optimized with respect to both the variational and design parameters. This
allows the design process to be carried out through a single unified stochastic
gradient ascent procedure, in contrast to existing approaches that typically
construct a pointwise EIG estimator, before passing this estimator to a
separate optimizer. We provide a number of different variational objectives
including the novel adaptive contrastive estimation (ACE) bound. Finally, we
show that our gradient-based approaches are able to provide effective design
optimization in substantially higher dimensional settings than existing
approaches.
