Jorge Cortés
Professor
Cymer Corporation Endowed Chair
Distributed optimization for multi-task learning via nuclear-norm approximation
D. Mateos-Nuñez, J. Cortés
IFAC Workshop on
Distributed Estimation and Control in Networked Systems, Philadelphia,
Pennsylvania, USA, 2015, vol. 48, issue 22, pp. 64-69
Abstract
We exploit a variational characterization of the nuclear norm to
extend the framework of distributed convex optimization to machine
learning problems that focus on the sparsity of the aggregate
solution. We propose two distributed dynamics that can be used
for multi-task feature learning and recommender systems in
scenarios with more tasks or users than features. Our first
dynamics tackles a convex minimization on local decision variables
subject to agreement on a set of local auxiliary matrices. Our
second dynamics employs a saddle-point reformulation through
Fenchel conjugation of quadratic forms, avoiding the computation
of the inverse of the local matrices. We establish the
correctness of both coordination algorithms using a general
analytical framework developed in our previous work that combines
distributed optimization and subgradient methods for saddle-point
problems.
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Mechanical and Aerospace Engineering,
University of California, San Diego
9500 Gilman Dr,
La Jolla, California, 92093-0411
Ph: 1-858-822-7930
Fax: 1-858-822-3107
cortes at ucsd.edu
Skype id:
jorgilliyo