mlsanityData to 14 Oct 2026

Uniform Error Bounds for Gaussian Process Regression with Application to Safe Control

arXiv 1906.01376 ↗First posted 4 Jun 2019cs.LG cs.SY eess.SYcited by 64

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Abstract (arXiv)

Data-driven models are subject to model errors due to limited and noisy training data. Key to the application of such models in safety-critical domains is the quantification of their model error. Gaussian processes provide such a measure and uniform error bounds have been derived, which allow safe control based on these models. However, existing error bounds require restrictive assumptions. In this paper, we employ the Gaussian process distribution and continuity arguments to derive a novel uniform error bound under weaker assumptions. Furthermore, we demonstrate how this distribution can be used to derive probabilistic Lipschitz constants and analyze the asymptotic behavior of our bound. Finally, we derive safety conditions for the control of unknown dynamical systems based on Gaussian process models and evaluate them in simulations of a robotic manipulator.

Key facts. Cited by 64 papers in the map (data through 14 Oct 2026). First posted on arXiv 4 Jun 2019.

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Citing papers per year: 2021: 10; 2022: 6; 2023: 12; 2024: 14; 2025: 12; 2026: 10.

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  1. 2021Practical and Rigorous Uncertainty Bounds for Gaussian Process Regressioncited by 49
  2. 2022Scaling ResNets in the Large-depth Regimecited by 18
  3. 2021Gaussian Process Uniform Error Bounds with Unknown Hyperparameters for Safety-Critical Applicationscited by 17
  4. 2024On Safety in Safe Bayesian Optimizationcited by 15
  5. 2021Robust Uncertainty Bounds in Reproducing Kernel Hilbert Spaces: A Convex Optimization Approachcited by 14
  6. 2021A New Representation of Successor Features for Transfer across Dissimilar Environmentscited by 13
  7. 2022Safe and Efficient Reinforcement Learning Using Disturbance-Observer-Based Control Barrier Functionscited by 11
  8. 2024Stopping Bayesian Optimization with Probabilistic Regret Boundscited by 11
  9. 2023Collaborative and Distributed Bayesian Optimization via Consensus: Showcasing the Power of Collaboration for Optimal Designcited by 9
  10. 2024Minimizing UCB: a Better Local Search Strategy in Local Bayesian Optimizationcited by 9
  11. 2021Residual Gaussian Process: A Tractable Nonparametric Bayesian Emulator for Multi-fidelity Simulationscited by 8
  12. 2023Can Learning Deteriorate Control? Analyzing Computational Delays in Gaussian Process-Based Event-Triggered Online Learningcited by 8
38 more
  1. 2021Uniform Error and Posterior Variance Bounds for Gaussian Process Regression with Application to Safe Controlcited by 7
  2. 2022Power of Quantum Generative Learningcited by 6
  3. 2024Error Bounds For Gaussian Process Regression Under Bounded Support Noise With Applications To Safety Certificationcited by 6
  4. 2021Formal Verification of Unknown Dynamical Systems via Gaussian Process Regressioncited by 5
  5. 2023Towards Safe Multi-Task Bayesian Optimizationcited by 5
  6. 2024Collaborative and Federated Black-box Optimization: A Bayesian Optimization Perspectivecited by 5
  7. 2025Finite-Sample-Based Reachability for Safe Control with Gaussian Process Dynamicscited by 5
  8. 2023Toward L_∞-recovery of Nonlinear Functions: A Polynomial Sample Complexity Bound for Gaussian Random Fieldscited by 4
  9. 2023Promises of Deep Kernel Learning for Control Synthesiscited by 4
  10. 2024Cooperative Learning with Gaussian Processes for Euler-Lagrange Systems Tracking Control under Switching Topologiescited by 4
  11. 2024Towards safe Bayesian optimization with Wiener kernel regressioncited by 4
  12. 2025On the convergence rate of noisy Bayesian Optimization with Expected Improvementcited by 4
  13. 2025The Hardness of Validating Observational Studies with Experimental Datacited by 4
  14. 2025Optimal kernel regression bounds under energy-bounded noisecited by 4
  15. 2025Streaming Generated Gaussian Process Experts for Online Learning and Control: Extended Versioncited by 4
  16. 2021Structure-Preserving Learning Using Gaussian Processes and Variational Integratorscited by 3
  17. 2023Safe Machine-Learning-supported Model Predictive Force and Motion Control in Roboticscited by 3
  18. 2023Learning-based Control for PMSM Using Distributed Gaussian Processes with Optimal Aggregation Strategycited by 3
  19. 2024Whom to Trust? Elective Learning for Distributed Gaussian Process Regressioncited by 3
  20. 2025SAD-Flower: Flow Matching for Safe, Admissible, and Dynamically Consistent Planningcited by 3
  21. 2022Networked Online Learning for Control of Safety-Critical Resource-Constrained Systems based on Gaussian Processescited by 2
  22. 2022Recursively Feasible Probabilistic Safe Online Learning with Control Barrier Functionscited by 2
  23. 2023CATE Estimation With Potential Outcome Imputation From Local Regressioncited by 2
  24. 2024Decision-Point Guided Safe Policy Improvementcited by 2
  25. 2025Distance-Aware Error for Spline Networks: A Bottom-Up Approach to Uncertaintycited by 2
  26. 2025Convergence Rates of Constrained Expected Improvementcited by 2
  27. 2025Enhancing Trust-Region Bayesian Optimization via Newton Methodscited by 2
  28. 2021Adaptive Low-Pass Filtering using Sliding Window Gaussian Processescited by 1
  29. 2022Barrier Certified Safety Learning Control: When Sum-of-Square Programming Meets Reinforcement Learningcited by 1
  30. 2023Stochastic Cell Transmission Models of Traffic Networkscited by 1
  31. 2024Gearing Gaussian process modeling and sequential design towards stochastic simulatorscited by 1
  32. 2024On Improved Regret Bounds In Bayesian Optimization with Gaussian Noisecited by 1
  33. 2025An Analysis of Safety Guarantees in Multi-Task Bayesian Optimizationcited by 1
  34. 2026Quality or Quantity? Error-Informed Selective Online Learning with Gaussian Processes in Multi-Agent Systems: Extended Versioncited by 1
  35. 2026Safe Reinforcement Learning via Recovery-based Shielding with Gaussian Process Dynamics Modelscited by 1
  36. 2026Safe learning-based control via function-based uncertainty quantificationcited by 1
  37. 2026Koopman operator theory: fundamentals, control, and applicationscited by 1
  38. 2021Guaranteed Trajectory Tracking under Learned Dynamics with Contraction Metrics and Disturbance Estimationcited by 0

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