%0 Generic %1 yang2016unified %A Yang, Tianbao %A Lin, Qihang %A Li, Zhe %D 2016 %K bayesian deeplearning optimization %T Unified Convergence Analysis of Stochastic Momentum Methods for Convex and Non-convex Optimization %U http://arxiv.org/abs/1604.03257 %X Recently, stochastic momentum methods have been widely adopted in training deep neural networks. However, their convergence analysis is still underexplored at the moment, in particular for non-convex optimization. This paper fills the gap between practice and theory by developing a basic convergence analysis of two stochastic momentum methods, namely stochastic heavy-ball method and the stochastic variant of Nesterov's accelerated gradient method. We hope that the basic convergence results developed in this paper can serve the reference to the convergence of stochastic momentum methods and also serve the baselines for comparison in future development. The novelty of convergence analysis presented in this paper is a unified framework, revealing more insights about the similarities and differences between different stochastic momentum methods and stochastic gradient method. The unified framework also exhibits a continuous change from the gradient method to Nesterov's accelerated gradient method and the heavy-ball method incurred by a free parameter. The theoretical and empirical results show that the stochastic variant of Nesterov's accelerated gradient method achieves a good tradeoff for optimizing deep neural networks among the three stochastic methods.

@misc{yang2016unified, abstract = {Recently, stochastic momentum methods have been widely adopted in training deep neural networks. However, their convergence analysis is still underexplored at the moment, in particular for non-convex optimization. This paper fills the gap between practice and theory by developing a basic convergence analysis of two stochastic momentum methods, namely stochastic heavy-ball method and the stochastic variant of Nesterov's accelerated gradient method. We hope that the basic convergence results developed in this paper can serve the reference to the convergence of stochastic momentum methods and also serve the baselines for comparison in future development. The novelty of convergence analysis presented in this paper is a unified framework, revealing more insights about the similarities and differences between different stochastic momentum methods and stochastic gradient method. The unified framework also exhibits a continuous change from the gradient method to Nesterov's accelerated gradient method and the heavy-ball method incurred by a free parameter. The theoretical and empirical results show that the stochastic variant of Nesterov's accelerated gradient method achieves a good tradeoff for optimizing deep neural networks among the three stochastic methods.}, added-at = {2016-04-13T09:40:08.000+0200}, author = {Yang, Tianbao and Lin, Qihang and Li, Zhe}, biburl = {https://www.bibsonomy.org/bibtex/289044d7aac58f3922f4c95520eebe56a/pixor}, description = {() - 1604.03257v1.pdf}, interhash = {ad3047f0baa3464c86c51eb8ba7b56cf}, intrahash = {89044d7aac58f3922f4c95520eebe56a}, keywords = {bayesian deeplearning optimization}, note = {cite arxiv:1604.03257v1.pdf}, timestamp = {2016-04-13T09:40:08.000+0200}, title = {Unified Convergence Analysis of Stochastic Momentum Methods for Convex and Non-convex Optimization}, url = {http://arxiv.org/abs/1604.03257}, year = 2016 }