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Online learning as an LQG optimal control problem with random matrices

Gnecco, Giorgio and Bemporad, Alberto and Gori, Marco and Morisi, Rita and Sanguineti, Marcello Online learning as an LQG optimal control problem with random matrices. In: 14th European Control Conference (ECC), July 15-17, 2015, Linz, Austria pp. 2482-2489. ISBN 978-3-9524269-3-7. (2015)

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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.

Item Type: Conference or Workshop Item (Paper)
Identification Number: 10.1109/ECC.2015.7330911
Uncontrolled Keywords: 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.
Subjects: Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Research Area: Computer Science and Applications
Depositing User: Caterina Tangheroni
Date Deposited: 26 Feb 2016 13:30
Last Modified: 26 Feb 2016 13:30
URI: http://eprints.imtlucca.it/id/eprint/3128

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