Safety Certification is Classification

2026-05-07

AI Summary

This work addresses the challenge of safety certification for dynamical systems under uncertainty by proposing a novel non-recursive approach that circumvents the error accumulation inherent in traditional dynamic programming over long time horizons, which often renders lower bounds on safety probabilities invalid. The method reformulates safety certification as a classification problem over trajectory data and introduces, for the first time, a kernel embedding framework to directly estimate T-step safety probabilities. This framework unifies existing paradigms such as barrier certificates and robust Markov models and extends naturally to non-Markovian systems. Experimental results on a neural network-controlled quadrotor demonstrate that the proposed approach yields stable and reliable safety guarantees in both long-horizon and non-Markovian settings, whereas conventional dynamic programming produces either vacuous or unsafe outcomes.

Abstract

The goal of this paper is certifying safety of dynamical systems subject to uncertainty. Existing approaches use trajectory data to estimate transition probabilities, and compute safety probabilities recursively via dynamic programming (DP). This recursion may lead to compounding errors in the certified safety probability, thus collapsing to a vacuous lower bound for growing horizons $T$. We propose a kernel embedding framework that treats safety certification as a classification problem on trajectory data, directly estimating the $T$-step safety probability without recursion. We show that the framework subsumes well-established approaches from the literature (e.g., barrier certificates, robust Markov models) as special cases, and allows us to go beyond their limitations. As the main consequence, it bypasses compounding error across the horizon and enables certification for systems with non-Markovian dynamics. We demonstrate that direct estimators remain stable independent of the certification horizon and in the non-Markovian setting, whilst DP-based certificates silently go unsound -- confirmed in simulation on a neural-controlled quadrotor.

Problem

• Safety Certification
• Dynamical Systems
• Uncertainty
• Non-Markovian Dynamics
• Trajectory Data

Innovation

• safety certification
• kernel embedding
• non-Markovian dynamics
• trajectory classification
• compounding error