Gradient descent only converges to minimizers

Jason D. Lee, Max Simchowitz, Michael I. Jordan, Benjamin Recht

Research output: Contribution to journalConference articlepeer-review

316 Scopus citations


We show that gradient descent converges to a local minimizer, almost surely with random initialization. This is proved by applying the Stable Manifold Theorem from dynamical systems theory.

Original languageEnglish (US)
Pages (from-to)1246-1257
Number of pages12
JournalJournal of Machine Learning Research
Issue numberJune
StatePublished - Jun 6 2016
Externally publishedYes
Event29th Conference on Learning Theory, COLT 2016 - New York, United States
Duration: Jun 23 2016Jun 26 2016

All Science Journal Classification (ASJC) codes

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


  • Gradient descent
  • Local minimum
  • Non-convex
  • Saddle points


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