Safety Certification as Classification via Kernel Embedding

A new arXiv paper (2605.06087) proposes reframing safety certification of dynamical systems under uncertainty as a classification problem. Existing methods use trajectory data to estimate transition probabilities and compute safety probabilities recursively via dynamic programming, which can lead to compounding errors and vacuous lower bounds for long horizons. The authors introduce a kernel embedding framework that directly estimates T-step safety probability without recursion, subsuming established approaches like barrier certificates and robust Markov models. This bypasses compounding errors and enables certification for non-Markovian dynamics. The paper demonstrates direct estimation of safety probabilities, offering a more robust alternative for systems with growing time horizons.