mlsanityData to 7 Oct 2026

Kernel-Based Learning of Safety Barriers

arXiv 2601.12002 ↗First posted 17 Jan 2026cs.AI cs.LG cs.SYcited by 0

Not on the map. Why?

Abstract (arXiv)

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.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 52 of its 95 references that are in the map. First posted on arXiv 17 Jan 2026.

Builds on

52 of 95 references.

References · 52

  1. 2021Convex optimizationcited by 2,479
  2. 2017Reluplex: An Efficient SMT Solver for Verifying Deep Neural Networkscited by 739
  3. 2016Safety Verification of Deep Neural Networkscited by 262
  4. 2018Gaussian Processes and Kernel Methods: A Review on Connections and Equivalencescited by 188
  5. 2020A Measure-Theoretic Approach to Kernel Conditional Mean Embeddingscited by 86
  6. 2022Optimal Rates for Regularized Conditional Mean Embedding Learningcited by 50
  7. 2020Non-parametric Models for Non-negative Functionscited by 40
  8. 2023How to Train Your Neural Control Barrier Function: Learning Safety Filters for Complex Input-Constrained Systemscited by 40
  9. 2022Learning with little mixingcited by 33
  10. 2017Safe Learning of Quadrotor Dynamics Using Barrier Certificatescited by 32
  11. 2019A Rigorous Theory of Conditional Mean Embeddingscited by 31
  12. 2022Learning linear operators: Infinite-dimensional regression as a well-behaved non-compact inverse problemcited by 27
38 more
  1. 2019Formal Synthesis of Stochastic Systems via Control Barrier Certificatescited by 21
  2. 2021Automated Verification and Synthesis of Stochastic Hybrid Systems: A Surveycited by 20
  3. 2020Control Barrier Functions for Unknown Nonlinear Systems using Gaussian Processescited by 19
  4. 2023Fossil 2.0: Formal Certificate Synthesis for the Verification and Control of Dynamical Modelscited by 15
  5. 2019A Barrier Function Approach to Finite-Time Stochastic System Verification and Controlcited by 14
  6. 2020Global Optimization of Gaussian processescited by 14
  7. 2020Hard Shape-Constrained Kernel Machinescited by 13
  8. 2021Data-driven verification and synthesis of stochastic systems via barrier certificatescited by 12
  9. 2024Formal Synthesis of Controllers for Safety-Critical Autonomous Systems: Developments and Challengescited by 12
  10. 2024Stochastic Omega-Regular Verification and Control with Supermartingalescited by 10
  11. 2024Data-Driven Distributionally Robust Safety Verification Using Barrier Certificates and Conditional Mean Embeddingscited by 9
  12. 2020Formal Policy Synthesis for Continuous-Space Systems via Reinforcement Learningcited by 8
  13. 2022Data-Driven Abstraction-Based Control Synthesiscited by 7
  14. 2022Maximum Mean Discrepancy Distributionally Robust Nonlinear Chance-Constrained Optimization with Finite-Sample Guaranteecited by 6
  15. 2023Distributionally Robust Optimal and Safe Control of Stochastic Systems via Kernel Conditional Mean Embeddingcited by 6
  16. 2023Simultaneous Synthesis and Verification of Neural Control Barrier Functions through Branch-and-Bound Verification-in-the-loop Trainingcited by 6
  17. 2018Bounding Multivariate Trigonometric Polynomials with Applications to Filter Bank Designcited by 5
  18. 2022Robust Control Barrier Functions for Nonlinear Control Systems with Uncertainty: A Duality-based Approachcited by 5
  19. 2023Bayesian Formal Synthesis of Unknown Systems via Robust Simulation Relationscited by 5
  20. 2024Safe Reach Set Computation via Neural Barrier Certificatescited by 5
  21. 2020Solving natural conic formulations with Hypatia.jlcited by 4
  22. 2022Unmatched Control Barrier Functions: Certainty Equivalence Adaptive Safetycited by 4
  23. 2023Generative Modeling of Residuals for Real-Time Risk-Sensitive Safety with Discrete-Time Control Barrier Functionscited by 4
  24. 2023Assume-Guarantee Reinforcement Learningcited by 4
  25. 2024textttimmrax: A Parallelizable and Differentiable Toolbox for Interval Analysis and Mixed Monotone Reachability in JAXcited by 4
  26. 2024A data-driven approach for safety quantification of non-linear stochastic systems with unknown additive noise distributioncited by 4
  27. 2023Data-driven abstractions via adaptive refinements and a Kantorovich metric [extended version]cited by 3
  28. 2024Formal Verification of Unknown Stochastic Systems via Non-parametric Estimationcited by 3
  29. 2024Data-Driven Permissible Safe Control with Barrier Certificatescited by 3
  30. 2024On the Consistency of Kernel Methods with Dependent Observationscited by 3
  31. 2024Data-Driven Abstractions via Binary-Tree Gaussian Processes for Formal Verificationcited by 3
  32. 2022Safety-Aware Learning-Based Control of Systems with Uncertainty Dependent Constraints (extended version)cited by 2
  33. 2023Neural Abstraction-Based Controller Synthesis and Deploymentcited by 2
  34. 2023Stochastic Control Barrier Functions with Bayesian Inference for Unknown Stochastic Differential Equationscited by 2
  35. 2025Data-Driven Yet Formal Policy Synthesis for Stochastic Nonlinear Dynamical Systemscited by 2
  36. 2025Distributionally Robust Control Synthesis for Stochastic Systems with Safety and Reach-Avoid Specificationscited by 2
  37. 2025LUCID: Learning-Enabled Uncertainty-Aware Certification of Stochastic Dynamical Systemscited by 2
  38. 2015Sampling algebraic varieties for sum of squares programscited by 1

50 most cited of 52 All 52 (JSON)

Built on by

Not cited yet.