Practical and Rigorous Uncertainty Bounds for Gaussian Process Regression

arXiv (Cornell University), vol. 35, pp. 7439–7447

Abstract

Gaussian Process Regression is a popular nonparametric regression method based on Bayesian principles that provides uncertainty estimates for its predictions. However, these estimates are of a Bayesian nature, whereas for some important applications, like learning-based control with safety guarantees, frequentist uncertainty bounds are required. Although such rigorous bounds are available for Gaussian Processes, they are too conservative to be useful in applications. This often leads practitioners to replacing these bounds by heuristics, thus breaking all theoretical guarantees. To address this problem, we introduce new uncertainty bounds that are rigorous, yet practically useful at the same time. In particular, the bounds can be explicitly evaluated and are much less conservative than state of the art results. Furthermore, we show that certain model misspecifications lead to only graceful degradation. We demonstrate these advantages and the usefulness of our results for learning-based control with numerical examples.

Authors 3

1. Christian Fiedler Aachen Institute for Data Science in Mechanical Engineering

   RWTH Aachen University · Max Planck Institute for Intelligent Systems · University of Stuttgart

   Affiliation as printed

   Institute for Data Science in Mechanical Engineering, RWTH Aachen University#N#Intelligent Control Systems Group, Max Planck Institute for Intelligent Systems#N#Department of Mathematics, University of Stuttgart

2. Carsten W. Scherer

   University of Stuttgart

   Affiliation as printed

   Mathematical Systems Theory , University of Stuttgart

   Department of Mathematics, University of Stuttgart

3. Sebastian Trimpe Aachen Institute for Data Science in Mechanical Engineering

   RWTH Aachen University · Max Planck Institute for Intelligent Systems

   Affiliation as printed

   Institute for Data Science in Mechanical Engineering , RWTH Aachen University

   Intelligent Control Systems Group , Max Planck Institute for Intelligent Systems

   Institute for Data Science in Mechanical Engineering, RWTH Aachen University#N#Intelligent Control Systems Group, Max Planck Institute for Intelligent Systems