A Comparison Study of Supervised Learning Techniques for the Approximation of High Dimensional Functions and Feedback Control

Approximation of high dimensional functions is in the focus of machine learning and data-based scientific computing. In many applications, empirical risk minimisation techniques over nonlinear model classes are employed. Neural networks, kernel methods and tensor decomposition techniques are among the most popular model classes. This work is targeted on providing a numerical study comparing the performance of these methods on various high-dimensional functions with focus on optimal control problems, where the collection of the dataset is based on the application of the State-Dependent Riccati Equation, an extension of the LQR technique to nonlinear systems and nonquadratic cost functionals.