Data-Driven Stochastic Optimal Control Using Kernel Gradients

We present an empirical, gradient-based method for solving data-driven stochastic optimal control problems using the theory of kernel embeddings of distributions. By embedding the integral operator of a stochastic kernel in a reproducing kernel Hilbert space (RKHS), we can compute an empirical approximation of stochastic optimal control problems, which can then be solved efficiently using the properties of the RKHS. Existing approaches typically rely upon finite control spaces or optimize over policies with finite support to enable optimization. In contrast, our approach uses kernel-based gradients computed using observed data to approximate the cost surface of the optimal control problem, which can then be optimized using gradient descent. We apply our technique to the area of data-driven stochastic optimal control, and demonstrate our proposed approach on a linear regulation problem for comparison and on a nonlinear target tracking problem.