SReachTools Kernel Module: Data-Driven Stochastic Reachability Using\n Hilbert Space Embeddings of Distributions

We present algorithms for performing data-driven stochastic reachability as\nan addition to SReachTools, an open-source stochastic reachability toolbox. Our\nmethod leverages a class of machine learning techniques known as kernel\nembeddings of distributions to approximate the safety probabilities for a wide\nvariety of stochastic reachability problems. By representing the probability\ndistributions of the system state as elements in a reproducing kernel Hilbert\nspace, we can learn the "best fit" distribution via a simple regularized\nleast-squares problem, and then compute the stochastic reachability safety\nprobabilities as simple linear operations. This technique admits finite sample\nbounds and has known convergence in probability. We implement these methods as\npart of SReachTools, and demonstrate their use on a double integrator system,\non a million-dimensional repeated planar quadrotor system, and a cart-pole\nsystem with a black-box neural network controller.\n