DeepAI
Log In Sign Up

Improved Analysis of Clipping Algorithms for Non-convex Optimization

10/05/2020
by   Bohang Zhang, et al.
0

Gradient clipping is commonly used in training deep neural networks partly due to its practicability in relieving the exploding gradient problem. Recently, <cit.> show that clipped (stochastic) Gradient Descent (GD) converges faster than vanilla GD/SGD via introducing a new assumption called (L_0, L_1)-smoothness, which characterizes the violent fluctuation of gradients typically encountered in deep neural networks. However, their iteration complexities on the problem-dependent parameters are rather pessimistic, and theoretical justification of clipping combined with other crucial techniques, e.g. momentum acceleration, are still lacking. In this paper, we bridge the gap by presenting a general framework to study the clipping algorithms, which also takes momentum methods into consideration. We provide convergence analysis of the framework in both deterministic and stochastic setting, and demonstrate the tightness of our results by comparing them with existing lower bounds. Our results imply that the efficiency of clipping methods will not degenerate even in highly non-smooth regions of the landscape. Experiments confirm the superiority of clipping-based methods in deep learning tasks.

READ FULL TEXT

page 4

page 5

page 6

page 7

page 33

page 36

page 37

page 40

08/10/2018

On the Convergence of AdaGrad with Momentum for Training Deep Neural Networks

Adaptive stochastic gradient descent methods, such as AdaGrad, Adam, Ada...
08/03/2022

SGEM: stochastic gradient with energy and momentum

In this paper, we propose SGEM, Stochastic Gradient with Energy and Mome...
10/01/2020

Understanding the Role of Momentum in Non-Convex Optimization: Practical Insights from a Lyapunov Analysis

Momentum methods are now used pervasively within the machine learning co...
08/30/2018

A Unified Analysis of Stochastic Momentum Methods for Deep Learning

Stochastic momentum methods have been widely adopted in training deep ne...
07/31/2022

Formal guarantees for heuristic optimization algorithms used in machine learning

Recently, Stochastic Gradient Descent (SGD) and its variants have become...
05/24/2018

Nonlinear Acceleration of Deep Neural Networks

Regularized nonlinear acceleration (RNA) is a generic extrapolation sche...