Scalable Gaussian Process Regression via Deterministic Trigonometric Features: Uniform Bounds for Safe Model Predictive Control

arXiv (Cornell University)

Abstract

Learning-based Model Predictive Control (MPC) using Gaussian processes (GPs) is an effective approach for safe control in the presence of model mismatch. High-probability safety guarantees typically require uncertainty bounds that hold uniformly over the entire state--input domain, but existing bounds are available only for full GP regression. Since exact GP inference scales poorly with the number of data points, its deployment is impractical in large-data regimes. We close this gap by developing a scalable GP framework that admits the derivation of uniform uncertainty bounds. We formalize a deterministic trigonometric feature Gaussian process (DTF-GP), a finite-dimensional kernel approximation based on discretized trigonometric features that reduces GP regression to Bayesian linear regression in feature space. We derive a high-probability uniform uncertainty bound for the proposed DTF-GP and provide its closed-form solution for the squared-exponential kernel case. Finally, we integrate the DTF-GP into a learning-based MPC scheme and demonstrate that it provides high-probability safety guarantees and exploration performance comparable to a full GP while improving computational efficiency in large-data regimes.

Authors 5

1. Julius Jagdt Aachen Institute for Data Science in Mechanical Engineering

   RWTH Aachen University

   Affiliation as printed

   Institute for Data Science in Mechanical Engineering , RWTH Aachen University , Germany

2. Johanna Menn Aachen Institute for Data Science in Mechanical Engineering

   RWTH Aachen University

   Affiliation as printed

   Institute for Data Science in Mechanical Engineering , RWTH Aachen University , Germany

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

   RWTH Aachen University

   Affiliation as printed

   Institute for Data Science in Mechanical Engineering , RWTH Aachen University , Germany

4. Melanie N. Zeilinger

   ETH Zurich · Institute for Dynamic Systems and Control

   Affiliation as printed

   Institute for Dynamic Systems and Control , ETH Zürich , Zürich , Switzerland

5. Anna Scampicchio

   Chalmers University of Technology

   Affiliation as printed

   Department of Electrical Engineering , Chalmers University of Technology , Göteborg , Sweden