%P 2482-2489
%T Online learning as an LQG optimal control problem with random matrices
%R 10.1109/ECC.2015.7330911
%C Linz, Austria
%L eprints3128
%I IEEE
%X In this paper, we combine optimal control theory and machine learning techniques to propose and solve an optimal control formulation of online learning from supervised examples, which are used to learn an unknown vector parameter modeling the relationship between the input examples and their outputs. We show some connections of the problem investigated with the classical LQG optimal control problem, of which the proposed problem is a non-trivial variation, as it involves random matrices. We also compare the optimal solution to the proposed problem with the Kalman-filter estimate of the parameter vector to be learned, demonstrating its larger smoothness and robustness to outliers. Extension of the proposed online-learning framework are mentioned at the end of the paper.
%K Kalman filters; Learning (artificial intelligence); Linear quadratic Gaussian control; Matrix algebra; Kalman-filter; LQG optimal control problem; Machine learning technique; Online-learning framework; Random matrices; Unknown vector parameter modeling; Mathematical model; Measurement uncertainty; Optimal control; Optimization; Random variables; Robustness; Time measurement.
%A Giorgio Gnecco
%A Alberto Bemporad
%A Marco Gori
%A Rita Morisi
%A Marcello Sanguineti
%D 2015
%B Proceedings of the 14th IEEE European Control Conference (ECC)