Journals & Publications

Title: Learning a Coupled Linearized Method in Online Setting

Authors: Xue, W; Zhang, WS

Author Full Names: Xue, Wei; Zhang, Wensheng

Source: IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS, 28 (2):438-450; 10.1109/TNNLS.2016.2514413 FEB 2017

Language: English

Abstract: Based on the alternating direction method of multipliers, in this paper, we propose, analyze, and test a coupled linearized method, which aims to minimize an unconstrained problem consisting of a loss term and a regularization term in an online setting. To solve this problem, we first transform it into an equivalent constrained minimization problem with a separable structure. Then, we split the corresponding augmented Lagrangian function and minimize the resulting subproblems distributedly with one variable by fixing another one. This method is easy to execute without calculating matrix inversion by implementing three linearized operations per iteration, and at each iteration, we can obtain a closed-form solution. In particular, our update rule contains the well-known soft-thresholding operator as a special case. Moreover, upper bound on the regret of the proposed method is analyzed. Under some mild conditions, it can achieve 0(1/ root T) convergence rate for convex learning problems and 0((logT)/ T) for strongly convex learning. Numerical experiments and comparisons with several state-of-the-art methods are reported, which demonstrate the efficiency and effectiveness of our approach.

ISSN: 2162-237X

eISSN: 2162-2388

IDS Number: EL3MJ

Unique ID: WOS:000394522900017

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