Provable Convergence of Nesterov Accelerated Method for Over-Parameterized Neural Networks

• URL: http://arxiv.org/abs/2107.01832v1
• Date: Mon, 5 Jul 2021 07:40:35 GMT
• Title: Provable Convergence of Nesterov Accelerated Method for Over-Parameterized Neural Networks
• Authors: Xin Liu and Zhisong Pan
• Abstract summary: We analyze NAG for two fully connected neural network with ReLU activation. We prove that the error of NAG to zero at a rate of Theta (1/sqrtkappa)$, where $kappa 1$ is determined by a rate of neural network.
• Score: 7.40653399983911
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Despite the empirical success of deep learning, it still lacks theoretical understandings to explain why randomly initialized neural network trained by first-order optimization methods is able to achieve zero training loss, even though its landscape is non-convex and non-smooth. Recently, there are some works to demystifies this phenomenon under over-parameterized regime. In this work, we make further progress on this area by considering a commonly used momentum optimization algorithm: Nesterov accelerated method (NAG). We analyze the convergence of NAG for two-layer fully connected neural network with ReLU activation. Specifically, we prove that the error of NAG converges to zero at a linear convergence rate $1-\Theta(1/\sqrt{\kappa})$, where $\kappa > 1$ is determined by the initialization and the architecture of neural network. Comparing to the rate $1-\Theta(1/\kappa)$ of gradient descent, NAG achieves an acceleration. Besides, it also validates NAG and Heavy-ball method can achieve a similar convergence rate.

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