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.

介绍了一种新的随机优化算法 - 基于正交面的近端随机梯度方法（OBProx-SG）- 用于解决最流行的稀疏正则化问题，与现有方法相比，在稀疏探索和目标值方面综合表现优异，特别是在凸优化问题上获得了全局最优解，同时在非凸优化问题上获得了稳定点，同时在非凸深度神经网络中获得了更高稀疏度的解而不会牺牲泛化精度。