Kernel-Based Learning of Safety Barriers

• URL: http://arxiv.org/abs/2601.12002v1
• Date: Sat, 17 Jan 2026 10:42:35 GMT
• Title: Kernel-Based Learning of Safety Barriers
• Authors: Oliver Schön, Zhengang Zhong, Sadegh Soudjani,
• Abstract summary: Rapid integration of AI algorithms in safety-critical applications is raising concerns about the ability to meet stringent safety standards.<n>Traditional tools for formal safety verification struggle with the black-box nature of AI-driven systems.<n>We present a data-driven approach for safety verification and synthesis of black-box systems with discrete-time dynamics.
• Score: 0.9367224590861915
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: The rapid integration of AI algorithms in safety-critical applications such as autonomous driving and healthcare is raising significant concerns about the ability to meet stringent safety standards. Traditional tools for formal safety verification struggle with the black-box nature of AI-driven systems and lack the flexibility needed to scale to the complexity of real-world applications. In this paper, we present a data-driven approach for safety verification and synthesis of black-box systems with discrete-time stochastic dynamics. We employ the concept of control barrier certificates, which can guarantee safety of the system, and learn the certificate directly from a set of system trajectories. We use conditional mean embeddings to embed data from the system into a reproducing kernel Hilbert space (RKHS) and construct an RKHS ambiguity set that can be inflated to robustify the result to out-of-distribution behavior. We provide the theoretical results on how to apply the approach to general classes of temporal logic specifications beyond safety. For the data-driven computation of safety barriers, we leverage a finite Fourier expansion to cast a typically intractable semi-infinite optimization problem as a linear program. The resulting spectral barrier allows us to leverage the fast Fourier transform to generate the relaxed problem efficiently, offering a scalable yet distributionally robust framework for verifying safety. Our work moves beyond restrictive assumptions on system dynamics and uncertainty, as demonstrated on two case studies including a black-box system with a neural network controller.

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