  We present an optimization-based approach to stochastic control problems with
nonclassical information structures. We cast these problems equivalently as
optimization prob- lems on joint distributions. The resulting problems are
necessarily nonconvex. Our approach to solving them is through convex
relaxation. We solve the instance solved by Bansal and Basar with a particular
application of this approach that uses the data processing inequality for
constructing the convex relaxation. Using certain f-divergences, we obtain a
new, larger set of inverse optimal cost functions for such problems. Insights
are obtained on the relation between the structure of cost functions and of
convex relaxations for inverse optimal control.
