Data-driven Minimization with Random Feature Expansions for Optical Beam Forming Network Tuning

This paper proposes a data-driven method to minimize objective functions which can be measured in practice but are difficult to model. In the proposed method, the objective is learned directly from training data using random feature expansions. On the theoretical side, it is shown that the learned objective does not suffer from artificial local minima far away from the minima of the true objective if the random basis expansions are fit well enough in the uniform sense. The method is also tested on a real-life application, the tuning of an optical beamforming network. It is found that, in the presence of small model errors, the proposed method outperforms the classical approach of modeling from first principles and then estimating the model parameters.