Special Properties of Gradient Descent with Large Learning Rates
This work addresses a fundamental issue in machine learning optimization for researchers and practitioners, providing a new theoretical framework for analyzing algorithm behaviors beyond traditional settings.
The paper tackles the problem of understanding why large learning rates are essential for training neural networks effectively, showing through experiments and formal proofs that large step sizes in gradient descent can lead to convergence to global minima instead of local ones in non-convex settings.
When training neural networks, it has been widely observed that a large step size is essential in stochastic gradient descent (SGD) for obtaining superior models. However, the effect of large step sizes on the success of SGD is not well understood theoretically. Several previous works have attributed this success to the stochastic noise present in SGD. However, we show through a novel set of experiments that the stochastic noise is not sufficient to explain good non-convex training, and that instead the effect of a large learning rate itself is essential for obtaining best performance.We demonstrate the same effects also in the noise-less case, i.e. for full-batch GD. We formally prove that GD with large step size -- on certain non-convex function classes -- follows a different trajectory than GD with a small step size, which can lead to convergence to a global minimum instead of a local one. Our settings provide a framework for future analysis which allows comparing algorithms based on behaviors that can not be observed in the traditional settings.