Efficiently Computable Safety Bounds for Gaussian Processes in Active Learning

Jörn Tebbe, Christoph Zimmer, Ansgar Steland, Markus Lange-Hegermann, Fabian Mies
Proceedings of The 27th International Conference on Artificial Intelligence and Statistics, PMLR 238:1333-1341, 2024.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v238-tebbe24a, title = {Efficiently Computable Safety Bounds for {G}aussian Processes in Active Learning}, author = {Tebbe, J\"{o}rn and Zimmer, Christoph and Steland, Ansgar and Lange-Hegermann, Markus and Mies, Fabian}, booktitle = {Proceedings of The 27th International Conference on Artificial Intelligence and Statistics}, pages = {1333--1341}, year = {2024}, editor = {Dasgupta, Sanjoy and Mandt, Stephan and Li, Yingzhen}, volume = {238}, series = {Proceedings of Machine Learning Research}, month = {02--04 May}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v238/tebbe24a/tebbe24a.pdf}, url = {https://proceedings.mlr.press/v238/tebbe24a.html}, 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.} }
Endnote
%0 Conference Paper %T Efficiently Computable Safety Bounds for Gaussian Processes in Active Learning %A Jörn Tebbe %A Christoph Zimmer %A Ansgar Steland %A Markus Lange-Hegermann %A Fabian Mies %B Proceedings of The 27th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2024 %E Sanjoy Dasgupta %E Stephan Mandt %E Yingzhen Li %F pmlr-v238-tebbe24a %I PMLR %P 1333--1341 %U https://proceedings.mlr.press/v238/tebbe24a.html %V 238 %X 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.
APA
Tebbe, J., Zimmer, C., Steland, A., Lange-Hegermann, M. & Mies, F.. (2024). Efficiently Computable Safety Bounds for Gaussian Processes in Active Learning. Proceedings of The 27th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 238:1333-1341 Available from https://proceedings.mlr.press/v238/tebbe24a.html.

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