Efficiently Computable Safety Bounds for Gaussian Processes in Active Learning

arXiv (Cornell University)

Abstract

Active learning of physical systems must commonly respect practical safety constraints, which restricts the exploration of the design space. Gaussian Processes (GPs) and their calibrated uncertainty estimations are widely used for this purpose. In many technical applications the design space is explored via continuous trajectories, along which the safety needs to be assessed. This is particularly challenging for strict safety requirements in GP methods, as it employs computationally expensive Monte-Carlo sampling of high quantiles. We address these challenges by providing provable safety bounds based on the adaptively sampled median of the supremum of the posterior GP. Our method significantly reduces the number of samples required for estimating high safety probabilities, resulting in faster evaluation without sacrificing accuracy and exploration speed. The effectiveness of our safe active learning approach is demonstrated through extensive simulations and validated using a real-world engine example.

Authors 5

1. Jörn Tebbe

   Ostwestfalen-Lippe University of Applied Sciences and Arts

   Affiliation as printed

   OWL University of Applied Sciences and Arts Bosch Center for Artificial Intelligence

2. Christoph Zimmer

   Ostwestfalen-Lippe University of Applied Sciences and Arts

   Affiliation as printed

   OWL University of Applied Sciences and Arts Bosch Center for Artificial Intelligence

3. Ansgar Steland Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University OWL University of Applied Sciences and Arts

4. Markus Lange‐Hegermann Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University OWL University of Applied Sciences and Arts

5. Fabian Mies

   Delft University of Technology

   Affiliation as printed

   TU Delft