  Kernel-based nonparametric models have become very attractive for model-based
control approaches for nonlinear systems. However, the selection of the kernel
and its hyperparameters strongly influences the quality of the learned model.
Classically, these hyperparameters are optimized to minimize the prediction
error of the model but this process totally neglects its later usage in the
control loop. In this work, we present a framework to optimize the kernel and
hyperparameters of a kernel-based model directly with respect to the
closed-loop performance of the model. Our framework uses Bayesian optimization
to iteratively refine the kernel-based model using the observed performance on
the actual system until a desired performance is achieved. We demonstrate the
proposed approach in a simulation and on a 3-DoF robotic arm.
