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arXiv · 1608.04826

A better convergence analysis of the block coordinate descent method for large scale machine learning

Ziqiang Shi·Rujie Liu
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Abstract

This paper considers the problems of unconstrained minimization of large scale smooth convex functions having block-coordinate-wise Lipschitz continuous gradients. The block coordinate descent (BCD) method are among the first optimization schemes suggested for solving such problems \cite{nesterov2012efficiency}. We obtain a new lower (to our best knowledge the lowest currently) bound that is $16p^3$ times smaller than the best known on the information-based complexity of BCD method based on an effective technique called Performance Estimation Problem (PEP) proposed by Drori and Teboulle \cite{drori2012performance} recently for analyzing the performance of first-order black box optimization methods. Numerical test confirms our analysis.

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Ziqiang Shi, Rujie Liu. 2016-08-17. A better convergence analysis of the block coordinate descent method for large scale machine learning. https://arxiv.org/abs/1608.04826

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