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Empirical risk minimization (ERM) problems express optimal classifiers as solutions of optimization problems in which the objective is the sum of a very large number of sample costs. Established approaches to solve ERM rely on computing stochastic gradient directions by accessing a single summand at each iteration. Despite the efficiency of individual iterations, these methods can be slow to converge and have convergence rates that are linear at best. In this talk we discuss approaches to adapt Newton and quasi-Newton methods for ERM problems. In the incremental quasi-Newton method we exploit memory to store curvature approximation matrices. We show that these curvature approximations succeed in approximating the Hessian and thereby lead to superlinear convergence. In the Adaptive Newton method we consider subsets of training samples that are augmented geometrically by a factor of two. Each time the training set is augmented we perform a single Newton step. We show that it is possible to achieve statistical accuracy with just two passes over the dataset.
Alejandro Ribeiro received the B.Sc. degree in electrical engineering from the Universidad de la Republica Oriental del Uruguay, Montevideo, in 1998 and the M.Sc. and Ph.D. degree in electrical engineering from the Department of Electrical and Computer Engineering, the University of Minnesota, Minneapolis in 2005 and 2007. From 1998 to 2003, he was a member of the technical staff at Bellsouth Montevideo. After his M.Sc. and Ph.D studies, in 2008 he joined the University of Pennsylvania (Penn), Philadelphia, where he is currently the Rosenbluth Associate Professor at the Department of Electrical and Systems Engineering. His research interests are in the applications of statistical signal processing to the study of networks and networked phenomena. His focus is on structured representations of networked data structures, graph signal processing,
network optimization, robot teams, and networked control. Dr. Ribeiro received the 2014 O. Hugo Schuck best paper award, and paper awards at the 2016 SSP Workshop, 2016 SAM Workshop, 2015 Asilomar SSC Conference, ACC 2013, ICASSP 2006, and ICASSP 2005. His teaching has been recognized with the 2017 Lindback award for distinguished teaching and the 2012 S. Reid Warren, Jr. Award presented by Penn's undergraduate student body for outstanding teaching. Dr. Ribeiro is a Fulbright scholar class of 2003 and a Penn Fellow class of 2015.