Generalization Performance of Multi-pass Stochastic Gradient Descent with Convex Loss Functions

Yunwen Lei, Ting Hu*, Ke Tang

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

19 Citations (Scopus)

Abstract

Stochastic gradient descent (SGD) has become the method of choice to tackle large-scale datasets due to its low computational cost and good practical performance. Learning rate analysis, either capacity-independent or capacity-dependent, provides a unifying viewpoint to study the computational and statistical properties of SGD, as well as the implicit regularization by tuning the number of passes. Existing capacity-independent learning rates require a nontrivial bounded subgradient assumption and a smoothness assumption to be optimal. Furthermore, existing capacity-dependent learning rates are only established for the specific least squares loss with a special structure. In this paper, we provide both optimal capacity-independent and capacity-dependent learning rates for SGD with general convex loss functions. Our results require neither bounded subgradient assumptions nor smoothness assumptions, and are stated with high probability. We achieve this improvement by a refined estimate on the norm of SGD iterates based on a careful martingale analysis and concentration inequalities on empirical processes.

Original languageEnglish
Number of pages41
JournalJournal of Machine Learning Research
Volume22
Publication statusPublished - Jan 2021

Scopus Subject Areas

  • Software
  • Control and Systems Engineering
  • Statistics and Probability
  • Artificial Intelligence

User-Defined Keywords

  • Generalization bound
  • Learning theory
  • Stochastic gradient descent

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