Model-Free Stochastic Reachability Using Kernel Distribution Embeddings

We present a data-driven solution to the terminal-hitting stochastic reachability problem for a Markov control process. We employ a nonparametric representation of the stochastic kernel as a conditional distribution embedding within a reproducing kernel Hilbert space (RKHS). This representation avoids intractable integrals in the dynamic recursion of the stochastic reachability problem since the expectations can be calculated as an inner product within the RKHS. We demonstrate this approach on a high-dimensional chain of integrators and on Clohessy-Wiltshire-Hill dynamics.