Mathematics > Optimization and Control
[Submitted on 10 Sep 2014 (v1), last revised 9 Sep 2015 (this version, v2)]
Title:Stochastic Primal-Dual Coordinate Method for Regularized Empirical Risk Minimization
View PDFAbstract:We consider a generic convex optimization problem associated with regularized empirical risk minimization of linear predictors. The problem structure allows us to reformulate it as a convex-concave saddle point problem. We propose a stochastic primal-dual coordinate (SPDC) method, which alternates between maximizing over a randomly chosen dual variable and minimizing over the primal variable. An extrapolation step on the primal variable is performed to obtain accelerated convergence rate. We also develop a mini-batch version of the SPDC method which facilitates parallel computing, and an extension with weighted sampling probabilities on the dual variables, which has a better complexity than uniform sampling on unnormalized data. Both theoretically and empirically, we show that the SPDC method has comparable or better performance than several state-of-the-art optimization methods.
Submission history
From: Lin Xiao [view email][v1] Wed, 10 Sep 2014 21:25:22 UTC (78 KB)
[v2] Wed, 9 Sep 2015 05:37:23 UTC (201 KB)
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