Optimal uncertainty bounds for multivariate kernel regression under bounded noise: a Gaussian process-based dual function
File(s)
Accepted version
Author(s)
Lahr, Amon
Scampicchio, Anna
Kohler, Johannes
Zeilinger, Melanie N
Type
Journal Article
Abstract
Non-conservative uncertainty bounds are essential for making reliable predictions about latent functions from noisy data—and thus, a key enabler for safe
learning-based control. In this domain, kernel methods
such as Gaussian process regression are established techniques, thanks to their inherent uncertainty quantification mechanism. Still, existing bounds either pose strong assumptions on the underlying noise distribution, are conservative, do not directly apply in the multi-output case, or are difficult to integrate into downstream tasks. This paper addresses these limitations by presenting a tight, deterministic bound for multi-output functions in Reproducing Kernel Hilbert Spaces (RKHSs) subject to bounded noise. It is obtained through an unconstrained, duality based formulation, which shares the same structure as classic Gaussian process confidence bounds, and canthus be straightforwardly integrated into downstream optimization pipelines. We show that the proposed bound generalizes existing results and illustrate its application using an example inspired by quadrotor dynamics learning.
learning-based control. In this domain, kernel methods
such as Gaussian process regression are established techniques, thanks to their inherent uncertainty quantification mechanism. Still, existing bounds either pose strong assumptions on the underlying noise distribution, are conservative, do not directly apply in the multi-output case, or are difficult to integrate into downstream tasks. This paper addresses these limitations by presenting a tight, deterministic bound for multi-output functions in Reproducing Kernel Hilbert Spaces (RKHSs) subject to bounded noise. It is obtained through an unconstrained, duality based formulation, which shares the same structure as classic Gaussian process confidence bounds, and canthus be straightforwardly integrated into downstream optimization pipelines. We show that the proposed bound generalizes existing results and illustrate its application using an example inspired by quadrotor dynamics learning.
Date Issued
2026-07-03
Date Acceptance
2026-06-15
Citation
IEEE Control Systems Letters, 2026, 10
ISSN
2475-1456
Publisher
Institute of Electrical and Electronics Engineers
Journal / Book Title
IEEE Control Systems Letters
Volume
10
Copyright Statement
Copyright © 2026 IEEE. This is the author’s accepted manuscript made available under a CC-BY licence in accordance with Imperial’s Research Publications Open Access policy (www.imperial.ac.uk/oa-policy)
License URL
Publication Status
Published
Date Publish Online
2026-07-03