  Safety is an essential asset when learning control policies for physical
systems, as violating safety constraints during training can lead to expensive
hardware damage. In response to this need, the field of safe learning has
emerged with algorithms that can provide probabilistic safety guarantees
without knowledge of the underlying system dynamics. Those algorithms often
rely on Gaussian process inference. Unfortunately, Gaussian process inference
scales cubically with the number of data points, limiting applicability to
high-dimensional and embedded systems. In this paper, we propose a safe
learning algorithm that provides probabilistic safety guarantees but leverages
the Nadaraya-Watson estimator instead of Gaussian processes. For the
Nadaraya-Watson estimator, we can reach logarithmic scaling with the number of
data points. We provide theoretical guarantees for the estimates, embed them
into a safe learning algorithm, and show numerical experiments on a simulated
seven-degrees-of-freedom robot manipulator.
