Uniform Error and Posterior Variance Bounds for Gaussian Process Regression with Application to Safe Control

01/13/2021
by   Armin Lederer, et al.
0

In application areas where data generation is expensive, Gaussian processes are a preferred supervised learning model due to their high data-efficiency. Particularly in model-based control, Gaussian processes allow the derivation of performance guarantees using probabilistic model error bounds. To make these approaches applicable in practice, two open challenges must be solved i) Existing error bounds rely on prior knowledge, which might not be available for many real-world tasks. (ii) The relationship between training data and the posterior variance, which mainly drives the error bound, is not well understood and prevents the asymptotic analysis. This article addresses these issues by presenting a novel uniform error bound using Lipschitz continuity and an analysis of the posterior variance function for a large class of kernels. Additionally, we show how these results can be used to guarantee safe control of an unknown dynamical system and provide numerical illustration examples.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 24

06/04/2019

Uniform Error Bounds for Gaussian Process Regression with Application to Safe Control

Data-driven models are subject to model errors due to limited and noisy ...
06/04/2019

Posterior Variance Analysis of Gaussian Processes with Application to Average Learning Curves

The posterior variance of Gaussian processes is a valuable measure of th...
11/25/2018

Robust Super-Level Set Estimation using Gaussian Processes

This paper focuses on the problem of determining as large a region as po...
09/06/2021

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

Gaussian processes have become a promising tool for various safety-criti...
06/14/2020

GP3: A Sampling-based Analysis Framework for Gaussian Processes

Although machine learning is increasingly applied in control approaches,...
11/20/2020

The Value of Data in Learning-Based Control for Training Subset Selection

Despite the existence of formal guarantees for learning-based control ap...
04/23/2020

Consistent Online Gaussian Process Regression Without the Sample Complexity Bottleneck

Gaussian processes provide a framework for nonlinear nonparametric Bayes...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.