In this paper, we propose a generic and simple strategy for utilizing stochastic gradient information in optimization. The technique essentially contains two consecutive steps in each iteration: 1) computing and normalizing each block (layer) of the mini-batch stochastic gradient; 2) selecting appropriate step size to update the decision variable (parameter) towards the negative of the block-normalized gradient. We conduct extensive empirical studies on various non-convex neural network optimization problems, including multi-layer perceptron, convolution neural networks and recurrent neural networks. The results indicate the block-normalized gradient can help accelerate the training of neural networks. In particular, we observe that the normalized gradient methods having constant step size with occasionally decay, such as SGD with momentum, have better performance in the deep convolution neural networks, while those with adaptive step sizes, such as Adam, perform better in recurrent neural networks. Besides, we also observe this line of methods can lead to solutions with better generalization properties, which is confirmed by the performance improvement over strong baselines.
Spectrally-normalized margin bounds for neural networks
University of California, Berkeley（加州大学伯克利分校）；Queensland University of Technology（昆士兰科技大学）；Cornell University（康奈尔大学）；University of Illinois, Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
Two-block vs. Multi-block ADMM: An empirical evaluation of convergence
Lawrence Livermore National Laboratory（劳伦斯利弗莫尔国家实验室）；College of Humanities and Sciences（人文与科学学院）；Northeast Normal University（东北师范大学）；University of Minnesota, Twin Cities（明尼苏达大学双城分校）
