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This paper proposes a new framework to compute finite-horizon safetyguarantees for discrete-time piece-wise affine systems with stochastic noise ofunknown distributions. The approach is based on a novel approach to synthesisea stochastic barrier function (SBF) from noisy data and rely on the scenariooptimization theory. In particular, we show that the stochastic program tosynthesize a SBF can be relaxed into a chance-constrained optimisation problemon which scenario approach theory applies. We further show that the resultingprogram can be reduced to a linear programming problem, thus guaranteeingefficiency. In contrast to existing approaches, this method is data efficientas it only requires the number of data to be proportional to the logarithm inthe negative inverse of the confidence level and is computationally efficientdue to its reduction to linear programming. The efficacy of the method isempirically evaluated on various verification benchmarks. Experiments show asignificant improvement with respect to state-of-the-art, obtaining tightercertificates with a confidence that is several orders of magnitude higher.

Inner approximations of stochastic programs for data-driven stochastic barrier function design