基于Orthant的近邻随机梯度法。

稀疏性导致的正则化问题在机器学习应用程序中无处不在，范围从特征选择到模型压缩。在本文中，我们提出了一种新颖的随机方法-基于Orthant的近邻随机梯度方法（OBProx-SG）-以解决最流行的实例，即l1正则化问题。..

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

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.