?url_ver=Z39.88-2004&rft_id=arXiv%3A1606.04272&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Adc&rft.relation=http%3A%2F%2Feprints.imtlucca.it%2F3142%2F&rft.title=Linear+Quadratic+Gaussian+(LQG)+online+learning&rft.creator=Gnecco%2C+Giorgio&rft.creator=Bemporad%2C+Alberto&rft.creator=Gori%2C+Marco&rft.creator=Sanguineti%2C+Marcello&rft.subject=QA75+Electronic+computers.+Computer+science&rft.description=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%2C+of+which+the+proposed+learning+paradigm+is+a+non+trivial+variation+as+it+involves+random+matrices%2C+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%2C+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%2C+including+the+infinite+learning+horizon+and%2C+via+the+so-called+%22kernel+trick%22%2C+the+case+of+nonlinear+models.%0D%0ASubjects%3A%09Optimization+and+Control+(math.OC)%0D%0ACite+as%3A%09arXiv%3A1606.04272+%5Bmath.OC%5D%0D%0A+%09(or+arXiv%3A1606.04272v2+%5Bmath.OC%5D+for+this+version)&rft.publisher=arXiv&rft.date=2016&rft.type=Working+Paper&rft.type=NonPeerReviewed&rft.format=application%2Fpdf&rft.language=en&rft.rights=cc_by_nc&rft.identifier=http%3A%2F%2Feprints.imtlucca.it%2F3142%2F1%2F1606.04272v2.pdf&rft.identifier=++Gnecco%2C+Giorgio+and+Bemporad%2C+Alberto+and+Gori%2C+Marco+and+Sanguineti%2C+Marcello++Linear+Quadratic+Gaussian+(LQG)+online+learning.++Working+Paper+++arXiv+++++++(Submitted)+++&rft.relation=https%3A%2F%2Farxiv.org%2Fabs%2F1606.04272&rft.relation=arXiv%3A1606.04272