TY - JOUR
T1 - On the linear convergence of the proximal gradient method for trace norm regularization
AU - Hou, Ke
AU - Zhou, Zirui
AU - So, Anthony Man Cho
AU - Luo, Zhi Quan
PY - 2013
Y1 - 2013
N2 - Motivated by various applications in machine learning, the problem of minimizing a convex smooth loss function with trace norm regularization has received much attention lately. Currently, a popular method for solving such problem is the proximal gradient method (PGM), which is known to have a sublinear rate of convergence. In this paper, we show that for a large class of loss functions, the convergence rate of the PGMis in fact linear. Our result is established without any strong convexity assumption on the loss function. A key ingredient in our proof is a new Lipschitzian error bound for the aforementioned trace norm-regularized problem, which may be of independent interest.
AB - Motivated by various applications in machine learning, the problem of minimizing a convex smooth loss function with trace norm regularization has received much attention lately. Currently, a popular method for solving such problem is the proximal gradient method (PGM), which is known to have a sublinear rate of convergence. In this paper, we show that for a large class of loss functions, the convergence rate of the PGMis in fact linear. Our result is established without any strong convexity assumption on the loss function. A key ingredient in our proof is a new Lipschitzian error bound for the aforementioned trace norm-regularized problem, which may be of independent interest.
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M3 - Conference article
AN - SCOPUS:84899032581
SN - 1049-5258
JO - Advances in Neural Information Processing Systems
JF - Advances in Neural Information Processing Systems
T2 - 27th Annual Conference on Neural Information Processing Systems, NIPS 2013
Y2 - 5 December 2013 through 10 December 2013
ER -