eprintid: 3142
rev_number: 12
eprint_status: archive
userid: 69
dir: disk0/00/00/31/42
datestamp: 2016-02-26 15:41:35
lastmod: 2016-10-04 09:03:37
status_changed: 2016-10-04 09:03:37
type: monograph
metadata_visibility: show
creators_name: Gnecco, Giorgio
creators_name: Bemporad, Alberto
creators_name: Gori, Marco
creators_name: Sanguineti, Marcello
creators_id: giorgio.gnecco@imtlucca.it
creators_id: alberto.bemporad@imtlucca.it
creators_id: 
creators_id: 
title: Linear Quadratic Gaussian (LQG) online learning
ispublished: submitted
subjects: QA75
divisions: CSA
full_text_status: public
monograph_type: working_paper
abstract: Optimal control theory and machine learning techniques are combined to propose and solve in closed form an optimal control formulation of online learning from supervised examples. The connections with the classical Linear Quadratic Gaussian (LQG) optimal control problem, of which the proposed learning paradigm is a non trivial variation as it involves random matrices, are investigated. The obtained optimal solutions are compared with the Kalman-filter estimate of the parameter vector to be learned. It is shown that the former enjoys larger smoothness and robustness to outliers, thanks to the presence of a regularization term. The basic formulation of the proposed online-learning framework refers to a discrete time setting with a finite learning horizon and a linear model. Various extensions are investigated, including the infinite learning horizon and, via the so-called "kernel trick", the case of nonlinear models.
Subjects:	Optimization and Control (math.OC)
Cite as:	arXiv:1606.04272 [math.OC]
 	(or arXiv:1606.04272v2 [math.OC] for this version)
date: 2016
date_type: submitted
publisher: arXiv
pages: 69
id_number: arXiv:1606.04272
institution: IMT Institute for Advanced Studies Lucca
refereed: FALSE
official_url: https://arxiv.org/abs/1606.04272
citation:   Gnecco, Giorgio and Bemporad, Alberto and Gori, Marco and Sanguineti, Marcello  Linear Quadratic Gaussian (LQG) online learning.  Working Paper   arXiv       (Submitted)   
document_url: http://eprints.imtlucca.it/3142/1/1606.04272v2.pdf