Stochastic extra-gradient based alternating direction methods for graph-guided regularized minimization

In this study, we propose and compare stochastic variants of the extra-gradient alternating direction method, named the stochastic extra-gradient alternating direction method with Lagrangian function (SEGL) and the stochastic extra-gradient alternating direction method with augmented Lagrangian function (SEGAL), to minimize the graph-guided optimization problems, which are composited with two convex objective functions in large scale. A number of important applications in machine learning follow the graph-guided optimization formulation, such as linear regression, logistic regression, Lasso, structured extensions of Lasso, and structured regularized logistic regression. We conduct experiments on fused logistic regression and graph-guided regularized regression. Experimental results on several genres of datasets demonstrate that the proposed algorithm outperforms other competing algorithms, and SEGAL has better performance than SEGL in practical use.