eprintid: 3128
rev_number: 5
eprint_status: archive
userid: 69
dir: disk0/00/00/31/28
datestamp: 2016-02-26 13:30:28
lastmod: 2016-02-26 13:30:28
status_changed: 2016-02-26 13:30:28
type: conference_item
metadata_visibility: show
creators_name: Gnecco, Giorgio
creators_name: Bemporad, Alberto
creators_name: Gori, Marco
creators_name: Morisi, Rita
creators_name: Sanguineti, Marcello
creators_id: giorgio.gnecco@imtlucca.it
creators_id: alberto.bemporad@imtlucca.it
creators_id: 
creators_id: rita.morisi@imtlucca.it
creators_id: 
title: Online learning as an LQG optimal control problem with random matrices
ispublished: pub
subjects: QA75
divisions: CSA
full_text_status: none
pres_type: paper
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.
abstract: 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.
date: 2015-07
date_type: published
publisher: IEEE
pagerange: 2482-2489
event_title: 14th European Control Conference (ECC)
event_location: Linz, Austria
event_dates: July 15-17, 2015
event_type: conference
id_number: 10.1109/ECC.2015.7330911
refereed: TRUE
isbn: 978-3-9524269-3-7
book_title: Proceedings of the 14th IEEE European Control Conference (ECC)
official_url: http://dx.doi.org/10.1109/ECC.2015.7330911
citation:   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)