Last-iterate convergence analysis of stochastic momentum methods for neural networks

• URL: http://arxiv.org/abs/2205.14811v1
• Date: Mon, 30 May 2022 02:17:44 GMT
• Title: Last-iterate convergence analysis of stochastic momentum methods for neural networks
• Authors: Dongpo Xu, Jinlan Liu, Yinghua Lu, Jun Kong, Danilo Mandic
• Abstract summary: The momentum method is used to solve large-scale optimization problems in neural networks. Current convergence results of momentum methods under artificial settings. The momentum factors can be fixed to be constant, rather than in existing time.
• Score: 3.57214198937538
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The stochastic momentum method is a commonly used acceleration technique for solving large-scale stochastic optimization problems in artificial neural networks. Current convergence results of stochastic momentum methods under non-convex stochastic settings mostly discuss convergence in terms of the random output and minimum output. To this end, we address the convergence of the last iterate output (called last-iterate convergence) of the stochastic momentum methods for non-convex stochastic optimization problems, in a way conformal with traditional optimization theory. We prove the last-iterate convergence of the stochastic momentum methods under a unified framework, covering both stochastic heavy ball momentum and stochastic Nesterov accelerated gradient momentum. The momentum factors can be fixed to be constant, rather than time-varying coefficients in existing analyses. Finally, the last-iterate convergence of the stochastic momentum methods is verified on the benchmark MNIST and CIFAR-10 datasets.

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