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Sparsity-inducing regularization problems are ubiquitous in machine learningapplications, ranging from feature selection to model compression. In thispaper, we present a novel stochastic method -- Orthant Based ProximalStochastic Gradient Method (OBProx-SG) -- to solve perhaps the most popularinstance, i.e., the l1-regularized problem. The OBProx-SG method contains twosteps: (i) a proximal stochastic gradient step to predict a support cover ofthe solution; and (ii) an orthant step to aggressively enhance the sparsitylevel via orthant face projection. Compared to the state-of-the-art methods,e.g., Prox-SG, RDA and Prox-SVRG, the OBProx-SG not only converges to theglobal optimal solutions (in convex scenario) or the stationary points (innon-convex scenario), but also promotes the sparsity of the solutionssubstantially. Particularly, on a large number of convex problems, OBProx-SGoutperforms the existing methods comprehensively in the aspect of sparsityexploration and objective values. Moreover, the experiments on non-convex deepneural networks, e.g., MobileNetV1 and ResNet18, further demonstrate itssuperiority by achieving the solutions of much higher sparsity withoutsacrificing generalization accuracy.

Orthant Based Proximal Stochastic Gradient Method for $\ell_1$-Regularized Optimization