  Hard visual attention is a promising approach to reduce the computational
burden of modern computer vision methodologies. Hard attention mechanisms are
typically non-differentiable. They can be trained with reinforcement learning
but the high-variance training this entails hinders more widespread
application. We show how hard attention for image classification can be framed
as a Bayesian optimal experimental design (BOED) problem. From this
perspective, the optimal locations to attend to are those which provide the
greatest expected reduction in the entropy of the classification distribution.
We introduce methodology from the BOED literature to approximate this optimal
behaviour, and use it to generate `near-optimal' sequences of attention
locations. We then show how to use such sequences to partially supervise, and
therefore speed up, the training of a hard attention mechanism. Although
generating these sequences is computationally expensive, they can be reused by
any other networks later trained on the same task.
