Gaussian Process Uniform Error Bounds with Unknown Hyperparameters for Safety-Critical Applications

Alexandre Capone, Armin Lederer, Sandra Hirche
Proceedings of the 39th International Conference on Machine Learning, PMLR 162:2609-2624, 2022.

Abstract

Gaussian processes have become a promising tool for various safety-critical settings, since the posterior variance can be used to directly estimate the model error and quantify risk. However, state-of-the-art techniques for safety-critical settings hinge on the assumption that the kernel hyperparameters are known, which does not apply in general. To mitigate this, we introduce robust Gaussian process uniform error bounds in settings with unknown hyperparameters. Our approach computes a confidence region in the space of hyperparameters, which enables us to obtain a probabilistic upper bound for the model error of a Gaussian process with arbitrary hyperparameters. We do not require to know any bounds for the hyperparameters a priori, which is an assumption commonly found in related work. Instead, we are able to derive bounds from data in an intuitive fashion. We additionally employ the proposed technique to derive performance guarantees for a class of learning-based control problems. Experiments show that the bound performs significantly better than vanilla and fully Bayesian Gaussian processes.

Cite this Paper

BibTeX
@InProceedings{pmlr-v162-capone22a, title = {{G}aussian Process Uniform Error Bounds with Unknown Hyperparameters for Safety-Critical Applications}, author = {Capone, Alexandre and Lederer, Armin and Hirche, Sandra}, booktitle = {Proceedings of the 39th International Conference on Machine Learning}, pages = {2609--2624}, year = {2022}, editor = {Chaudhuri, Kamalika and Jegelka, Stefanie and Song, Le and Szepesvari, Csaba and Niu, Gang and Sabato, Sivan}, volume = {162}, series = {Proceedings of Machine Learning Research}, month = {17--23 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v162/capone22a/capone22a.pdf}, url = {https://proceedings.mlr.press/v162/capone22a.html}, abstract = {Gaussian processes have become a promising tool for various safety-critical settings, since the posterior variance can be used to directly estimate the model error and quantify risk. However, state-of-the-art techniques for safety-critical settings hinge on the assumption that the kernel hyperparameters are known, which does not apply in general. To mitigate this, we introduce robust Gaussian process uniform error bounds in settings with unknown hyperparameters. Our approach computes a confidence region in the space of hyperparameters, which enables us to obtain a probabilistic upper bound for the model error of a Gaussian process with arbitrary hyperparameters. We do not require to know any bounds for the hyperparameters a priori, which is an assumption commonly found in related work. Instead, we are able to derive bounds from data in an intuitive fashion. We additionally employ the proposed technique to derive performance guarantees for a class of learning-based control problems. Experiments show that the bound performs significantly better than vanilla and fully Bayesian Gaussian processes.} }
Endnote
%0 Conference Paper %T Gaussian Process Uniform Error Bounds with Unknown Hyperparameters for Safety-Critical Applications %A Alexandre Capone %A Armin Lederer %A Sandra Hirche %B Proceedings of the 39th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2022 %E Kamalika Chaudhuri %E Stefanie Jegelka %E Le Song %E Csaba Szepesvari %E Gang Niu %E Sivan Sabato %F pmlr-v162-capone22a %I PMLR %P 2609--2624 %U https://proceedings.mlr.press/v162/capone22a.html %V 162 %X Gaussian processes have become a promising tool for various safety-critical settings, since the posterior variance can be used to directly estimate the model error and quantify risk. However, state-of-the-art techniques for safety-critical settings hinge on the assumption that the kernel hyperparameters are known, which does not apply in general. To mitigate this, we introduce robust Gaussian process uniform error bounds in settings with unknown hyperparameters. Our approach computes a confidence region in the space of hyperparameters, which enables us to obtain a probabilistic upper bound for the model error of a Gaussian process with arbitrary hyperparameters. We do not require to know any bounds for the hyperparameters a priori, which is an assumption commonly found in related work. Instead, we are able to derive bounds from data in an intuitive fashion. We additionally employ the proposed technique to derive performance guarantees for a class of learning-based control problems. Experiments show that the bound performs significantly better than vanilla and fully Bayesian Gaussian processes.
APA
Capone, A., Lederer, A. & Hirche, S.. (2022). Gaussian Process Uniform Error Bounds with Unknown Hyperparameters for Safety-Critical Applications. Proceedings of the 39th International Conference on Machine Learning, in Proceedings of Machine Learning Research 162:2609-2624 Available from https://proceedings.mlr.press/v162/capone22a.html.

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