Online learning in closed loop control systems is very attractive because it allows the automated identification of highly nonlinear dynamical systems as well as a fast adaptation to dynamically changing environments. Yet, depending on the application the data collection and the training of models is costly if not even prohibitive. On the one hand, the training is computationally expensive and might compromise real-time performance. In particular in non-parametric learning approaches as e.g. in Gaussian Processes, the computational tractability is tied to the number of training data. As such it is important to understand how informative training samples are and further how to improve algorithmic efficiency of training and prediction. In this talk we will demonstrate that the control task in addition to the underlying system dynamics has a strong influence on the required sample complexity. Employing Bayesian principles, we explore methods to quantify epistemic uncertainty with respect to control objectives and how they can be exploited to achieve a high sample efficiency for learning in the closed loop system. Additionally, approaches for efficient non-parametric online learning algorithms are proposed to allow the application of the presented methods under real-time constraints.
