Learning Functions and Uncertainty Sets Using Geometrically Constrained Kernel Regression

Christian Fiedler, Carsten W. Scherer, Sebastian Trimpe

Abstract: Learning-based control offers the potential to tackle challenging control problems and hence receives a lot of attention, both from the control and machine learning communities. To provide rigorous control-theoretic guarantees like stability or other safety-related properties, most of these approaches require a quantification of the uncertainty that is inevitable when learning from real data. Unfortunately, many existing methods rely on unrealistic assumptions to derive such uncertainty bounds, preventing the real-world usage of learning-based control. We focus on the regression setting and propose a new approach that only needs assumptions that can be derived from reasonable engineering knowledge. In order to achieve this goal, we combine the recently introduced Hard Shape Constrained Kernel Machines with geometric assumptions expressing prior model knowledge. The resulting algorithms can compute both nominal predictions with prescribed properties and rather tight uncertainty sets. Numerical experiments, including an illustrative control example, demonstrate the feasibility and performance of our approach.