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We present an optimization-based approach to stochastic control problems with nonclassical information structures. We cast these problems equivalently as optimization problems 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 Başar  with a particular application of this approach that uses the data processing inequality for constructing the convex relaxation. Insights are obtained on the relation between the structure of cost functions and of convex relaxations for inverse optimal control.