An Optimizer's Approach to Stochastic Control Problems With Nonclassical Information Structures

We present a general optimization-based framework for 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 (“Stochastic teams with nonclassical information revisited: When is an affine law optimal?”, IEEE Trans. Automatic Control, 1987) 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.