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

2021/09/06 by Alexandre Capone, Capone, Alexandre, Armin Lederer +3 · 2 citations
Computer Science · Engineering · #Advanced Control Systems Optimization #Control Systems and Identification #FOS: Computer and information sciences #FOS: Electrical engineering #Fault Detection and Control Systems #Gaussian Processes and Bayesian Inference #Machine Learning (cs.LG) #Robotics (cs.RO) #Systems and Control (eess.SY) #electronic engineering #information engineering

paper · pdf · doi:10.48550/arxiv.2109.02606

openalex publication_date 2021/09/06 · openalex created_date 2022/07/23 · openalex updated_date 2026/07/28

Abstract

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

Citations

• Safe Model-based Reinforcement Learning with Stability Guarantees
• GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Acceleration
• Uncertainty-aware Safe Exploratory Planning using Gaussian Process and Neural Control Contraction Metric
• Practical and Rigorous Uncertainty Bounds for Gaussian Process\n Regression

Cited by

• Adaptive Individual Uncertainty under Out-Of-Distribution Shift with Expert-Routed Conformal Prediction
• A Hierarchical Surrogate Model for Efficient Multi-Task Parameter Learning in Closed-Loop Control

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