On optimal probabilities in stochastic coordinate descent methods

Peter Richtárik, Martin Takáč*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

47 Scopus citations


We propose and analyze a new parallel coordinate descent method—NSync—in which at each iteration a random subset of coordinates is updated, in parallel, allowing for the subsets to be chosen using an arbitrary probability law. This is the first method of this type. We derive convergence rates under a strong convexity assumption, and comment on how to assign probabilities to the sets to optimize the bound. The complexity and practical performance of the method can outperform its uniform variant by an order of magnitude. Surprisingly, the strategy of updating a single randomly selected coordinate per iteration—with optimal probabilities—may require less iterations, both in theory and practice, than the strategy of updating all coordinates at every iteration.

Original languageEnglish (US)
Pages (from-to)1233-1243
Number of pages11
JournalOptimization Letters
Issue number6
StatePublished - Aug 1 2016
Externally publishedYes


  • Arbitrary sampling
  • Complexity
  • Coordinate descent
  • First order method

ASJC Scopus subject areas

  • Control and Optimization


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