Generalization Performance of Empirical Risk Minimization on Over-parameterized Deep ReLU Nets

Abstract

In this paper, we study the generalization performance of global minima for implementing empirical risk minimization (ERM) on over-parameterized deep ReLU nets. Using a novel deepening scheme for deep ReLU nets, we rigorously prove that there exist perfect global minima achieving almost optimal generalization error bounds for numerous types of data under mild conditions. Since over-parameterization is crucial to guarantee that the global minima of ERM on deep ReLU nets can be realized by the widely used stochastic gradient descent (SGD) algorithm, our results indeed fill a gap between optimization and generalization.

15 pages, 3 figures

References in corpus (8)

• Reconciling modern machine learning practice and the bias-variance trade-off
• Understanding deep learning requires rethinking generalization
• Benign Overfitting in Linear Regression
• Generalization Bounds of Stochastic Gradient Descent for Wide and Deep Neural Networks
• Complexity, Statistical Risk, and Metric Entropy of Deep Nets Using Total Path Variation
• Over-parametrized deep neural networks do not generalize well
• Norm-based generalisation bounds for multi-class convolutional neural networks
• Kernel Interpolation of High Dimensional Scattered Data