  Kernel embeddings of distributions have recently gained significant attention
in the machine learning community as a data-driven technique for representing
probability distributions. Broadly, these techniques enable efficient
computation of expectations by representing integral operators as elements in a
reproducing kernel Hilbert space. We apply these techniques to the area of
stochastic optimal control theory and present a method to compute approximately
optimal policies for stochastic systems with arbitrary disturbances. Our
approach reduces the optimization problem to a linear program, which can easily
be solved via the Lagrangian dual, without resorting to gradient-based
optimization algorithms. We focus on discrete-time dynamic programming, and
demonstrate our proposed approach on a linear regulation problem, and on a
nonlinear target tracking problem. This approach is broadly applicable to a
wide variety of optimal control problems, and provides a means of working with
stochastic systems in a data-driven setting.
