2020/10/05 by Bohang Zhang, Zhang, Bohang, Jikai Jin +5 · 22 citations
Computer Science · Mathematics · #Advanced Neural Network Applications #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Optimization and Control (math.OC) #Privacy-Preserving Technologies in Data #Stochastic Gradient Optimization Techniques #cs.LG #math.OC #stat.ML
paper · pdf · doi:10.48550/arxiv.2010.02519
41 pages, 12 figures, to appear in NeurIPS 2020. arXiv admin note: text overlap with arXiv:1905.11881 by other authors
openalex publication_date 2020/10/05 · arxiv created 2020/10/29 · arxiv updated 2020/10/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Gradient clipping is commonly used in training deep neural networks partly due to its practicability in relieving the exploding gradient problem. Recently, \citetzhang2019gradient show that clipped (stochastic) Gradient Descent (GD) converges faster than vanilla GD/SGD via introducing a new assumption called (L0, L1)-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.