Online Seminar Computer Science - Dr. Armin Lederer, ETH Zurich

Title: Safe and Computationally Efficient Online Learning Control using Gaussian Processes

Abstract:

In many real-world applications, the system models employed in control are unknown or merely partially known, e.g, due to complex environmental effects found in aerial and underwater robotics, or the lack of first principle models in human-robot interaction. In order to achieve a high control performance despite this model inaccuracy, supervised machine learning is commonly employed to improve the model precision. In this talk, we focus on Gaussian process regression for inferring a model of the system dynamics due to its strong statistical foundations and present the first computable probabilistic prediction error bound. This error bound admits a pessimistic analysis of the control performance, which we exemplarily demonstrate by deriving a tracking error bound for linear systems with unknown input perturbation. Due to the strong dependency of these results on the model uncertainty, we can show that arbitrarily small tracking errors can be guaranteed by updating the Gaussian process model online with a sufficiently high frequency. In order to achieve high model update rates, we propose a computationally efficient approximation for Gaussian process regression based on a local model aggregation. Since the proposed approximation maintains relevant theoretical guarantees of exact Gaussian process regression, performance guarantees for control directly extend to it. The effectiveness of the proposed approximation is demonstrated in regression problems with large real-world data sets and an experiment, in which humans physically interacting with a learning system act as perturbations.