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Training deep neural networks (DNNs) is an important and challengingoptimization problem in machine learning due to its non-convexity andnon-separable structure. The alternating minimization (AM) approaches split thecomposition structure of DNNs and have drawn great interest in the deeplearning and optimization communities. In this paper, we propose a unifiedframework for analyzing the convergence rate of AM-type network trainingmethods. Our analysis is based on the non-monotone $j$-step sufficient decreaseconditions and the Kurdyka-Lojasiewicz (KL) property, which relaxes therequirement of designing descent algorithms. We show the detailed localconvergence rate if the KL exponent $\theta$ varies in $[0,1)$. Moreover, thelocal R-linear convergence is discussed under a stronger $j$-step sufficientdecrease condition.

Convergence Rates of Training Deep Neural Networks via Alternating Minimization Methods