Gradient primal-dual algorithm converges to second-order stationary solution for nonconvex distributed optimization over networks

Mingyi Hong, Jason D. Lee, Meisam Razaviyayn

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Scopus citations

Abstract

In this work, we study two first-order primal-dual based algorithms, the Gradient Primal-Dual Algorithm (GPDA) and the Gradient Alternating Direction Method of Multipliers (GADMM), for solving a class of linearly constrained non-convex optimization problems. We show that with random initialization of the primal and dual variables, both algorithms are able to compute second-order stationary solutions (ss2) with probability one. This is the first result showing that primal-dual algorithm is capable of finding ss2 when only using first-order information; it also extends the existing results for first-order, but primal-only algorithms. An important implication of our result is that it also gives rise to the first global convergence result to the ss2, for two classes of unconstrained distributed non-convex learning problems over multi-agent networks.

Original languageEnglish (US)
Title of host publication35th International Conference on Machine Learning, ICML 2018
EditorsJennifer Dy, Andreas Krause
PublisherInternational Machine Learning Society (IMLS)
Pages3189-3198
Number of pages10
ISBN (Electronic)9781510867963
StatePublished - Jan 1 2018
Externally publishedYes
Event35th International Conference on Machine Learning, ICML 2018 - Stockholm, Sweden
Duration: Jul 10 2018Jul 15 2018

Publication series

Name35th International Conference on Machine Learning, ICML 2018
Volume5

Other

Other35th International Conference on Machine Learning, ICML 2018
CountrySweden
CityStockholm
Period7/10/187/15/18

All Science Journal Classification (ASJC) codes

  • Computational Theory and Mathematics
  • Human-Computer Interaction
  • Software

Cite this

Hong, M., Lee, J. D., & Razaviyayn, M. (2018). Gradient primal-dual algorithm converges to second-order stationary solution for nonconvex distributed optimization over networks. In J. Dy, & A. Krause (Eds.), 35th International Conference on Machine Learning, ICML 2018 (pp. 3189-3198). (35th International Conference on Machine Learning, ICML 2018; Vol. 5). International Machine Learning Society (IMLS).