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

• URL: http://arxiv.org/abs/2004.03639v2
• Date: Thu, 23 Jul 2020 04:54:42 GMT
• Title: Orthant Based Proximal Stochastic Gradient Method for $\ell_1$-Regularized Optimization
• Authors: Tianyi Chen, Tianyu Ding, Bo Ji, Guanyi Wang, Jing Tian, Yixin Shi, Sheng Yi, Xiao Tu, Zhihui Zhu
• Abstract summary: Sparsity-inducing regularization problems are ubiquitous in machine learning applications. We present a novel method -- Orthanximal Gradient Method (OBProx-SG)
• Score: 35.236001071182855
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Sparsity-inducing regularization problems are ubiquitous in machine learning applications, ranging from feature selection to model compression. In this paper, we present a novel stochastic method -- Orthant Based Proximal Stochastic Gradient Method (OBProx-SG) -- to solve perhaps the most popular instance, i.e., the l1-regularized problem. The OBProx-SG method contains two steps: (i) a proximal stochastic gradient step to predict a support cover of the solution; and (ii) an orthant step to aggressively enhance the sparsity level 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 the global optimal solutions (in convex scenario) or the stationary points (in non-convex scenario), but also promotes the sparsity of the solutions substantially. Particularly, on a large number of convex problems, OBProx-SG outperforms the existing methods comprehensively in the aspect of sparsity exploration and objective values. Moreover, the experiments on non-convex deep neural networks, e.g., MobileNetV1 and ResNet18, further demonstrate its superiority by achieving the solutions of much higher sparsity without sacrificing generalization accuracy.

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