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

• DOI: 10.1016/j.neucom.2023.01.032
• Publication Date: 2023-01-13T07:57:27Z
• Authors: Jinlan Liu; Dongpo Xu; Yinghua Lu; Jun Kong; Danilo P. Mandic
• Keywords: Iterated function; Momentum (technical analysis); Stochastic Gradient Descent; Stochastic Approximation

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.<br/>21pages, 4figures<br/>