On the low-rank approach for semidefinite programs arising in synchronization and community detection

Afonso S. Bandeira, Nicolas Boumal, Vladislav Voroninski

Research output: Contribution to journalConference article

Abstract

To address difficult optimization problems, convex relaxations based on semidefinite programming are now common place in many fields. Although solvable in polynomial time, large semidefinite programs tend to be computationally challenging. Over a decade ago, exploiting the fact that in many applications of interest the desired solutions are low rank, Burer and Monteiro proposed a heuristic to solve such semidefinite programs by restricting the search space to low-rank matrices. The accompanying theory does not explain the extent of the empirical success. We focus on Synchronization and Community Detection problems and provide theoretical guarantees shedding light on the remarkable efficiency of this heuristic.

Original languageEnglish (US)
Pages (from-to)361-382
Number of pages22
JournalJournal of Machine Learning Research
Volume49
Issue numberJune
StatePublished - Jun 6 2016
Event29th Conference on Learning Theory, COLT 2016 - New York, United States
Duration: Jun 23 2016Jun 26 2016

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Keywords

  • Burer-Monteiro heuristic
  • Community Detection
  • SDPLR
  • Semidefinite Programming
  • Synchronization

ASJC Scopus subject areas

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

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