  We present a novel stochastic approach to binary optimization for optimal
experimental design (OED) for Bayesian inverse problems governed by
mathematical models such as partial differential equations. The OED utility
function, namely, the regularized optimality criterion, is cast into a
stochastic objective function in the form of an expectation over a multivariate
Bernoulli distribution. The probabilistic objective is then solved by using a
stochastic optimization routine to find an optimal observational policy. The
proposed approach is analyzed from an optimization perspective and also from a
machine learning perspective with correspondence to policy gradient
reinforcement learning. The approach is demonstrated numerically by using an
idealized two-dimensional Bayesian linear inverse problem, and validated by
extensive numerical experiments carried out for sensor placement in a parameter
identification setup.
