Data-Driven Stochastic Reachability Using Hilbert Space Embeddings

We compute finite sample bounds for approximations of the solution to stochastic reachability problems computed using kernel distribution embeddings, a non-parametric machine learning technique. Our approach enables assurances of safety from observed data, through construction of probabilistic violation bounds on the computed stochastic reachability probability. By embedding the stochastic kernel of a Markov control process in a reproducing kernel Hilbert space, we can compute the safety probabilities for systems with arbitrary disturbances as simple matrix operations and inner products. We present finite sample bounds for the approximation using elements from statistical learning theory. We numerically evaluate the approach, and demonstrate its efficacy on neural net-controlled pendulum system.