Efficiently Computable Safety Bounds for Gaussian Processes in Active Learning


Conference paper


Jörn Tebbe, Christoph Zimmer, Ansgar Steland, Markus Lange-Hegermann, Fabian Mies
AISTATS, 2024

arXiv
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Cite

APA   Click to copy
Tebbe, J., Zimmer, C., Steland, A., Lange-Hegermann, M., & Mies, F. (2024). Efficiently Computable Safety Bounds for Gaussian Processes in Active Learning.


Chicago/Turabian   Click to copy
Tebbe, Jörn, Christoph Zimmer, Ansgar Steland, Markus Lange-Hegermann, and Fabian Mies. “Efficiently Computable Safety Bounds for Gaussian Processes in Active Learning.” AISTATS, 2024.


MLA   Click to copy
Tebbe, Jörn, et al. Efficiently Computable Safety Bounds for Gaussian Processes in Active Learning. 2024.


BibTeX   Click to copy

@inproceedings{joern2024a,
  title = {Efficiently Computable Safety Bounds for Gaussian Processes in Active Learning},
  year = {2024},
  series = {AISTATS},
  author = {Tebbe, Jörn and Zimmer, Christoph and Steland, Ansgar and Lange-Hegermann, Markus and Mies, Fabian}
}

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.

Transforming a non-centered Gaussian process to a heteroskedastic, centered Gaussian process



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