State-based confidence bounds for data-driven stochastic reachability using Hilbert space embeddings

In this paper, we compute finite sample bounds for data-driven approximations of the solution to stochastic reachability problems. Our approach uses a nonparametric technique known as kernel distribution embeddings, and provides probabilistic assurances safety systems in model-free manner. By implicitly embedding Markov control process reproducing Hilbert space, can approximate probabilities with arbitrary disturbances simple matrix operations inner products. We present point-based through construction confidence that are state- input-dependent. One advantage is responsive non-uniformly sampled data, meaning tighter feasible regions input-space more observations. numerically evaluate approach, demonstrate its efficacy on neural network-controlled pendulum system.