Title: A Half-Space Stochastic Projected Gradient Method for Group Sparsity Regularization. Abstract: Optimizing with group sparsity is significant in enhancing model interpretability in machining learning applications, e.g., feature selection, compressed sensing and model compression.  However, for large-scale stochastic training problems, effective group-sparsity exploration are typically hard to achieve. Particularly, the state-of-the-art stochastic optimization algorithms usually generate merely dense solutions. To overcome this shortage, we propose a stochastic method—Half-space Stochastic Projected Gradient method (HSPG) to search solutions of high group sparsity while maintain the convergence. Initialized by a simple Prox-SG Step, the HSPG method relies on a novel Half-Space Step to substantially boosts the sparsity level.  Numerically, HSPG demonstrates its superiority in deep neural networks, e.g., VGG16, ResNet18 and MobileNetV1, by computing solutions of higher group sparsity, competitive objective values and generalization accuracy.