Basis Matters: Better Communication-Efficient Second Order Methods for Federated Learning

Xun Qian, Rustem Islamov, Mher Safaryan, Peter Richtárik

Research output: Contribution to conferencePaperpeer-review

5 Scopus citations

Abstract

Recent advances in distributed optimization have shown that Newton-type methods with proper communication compression mechanisms can guarantee fast local rates and low communication cost compared to first order methods. We discover that the communication cost of these methods can be further reduced, sometimes dramatically so, with a surprisingly simple trick: Basis Learn (BL). The idea is to transform the usual representation of the local Hessians via a change of basis in the space of matrices and apply compression tools to the new representation. To demonstrate the potential of using custom bases, we design a new Newton-type method (BL1), which reduces communication cost via both BL technique and bidirectional compression mechanism. Furthermore, we present two alternative extensions (BL2 and BL3) to partial participation to accommodate federated learning applications. We prove local linear and superlinear rates independent of the condition number. Finally, we support our claims with numerical experiments by comparing several first and second order methods.

Original languageEnglish (US)
Pages680-720
Number of pages41
StatePublished - 2022
Event25th International Conference on Artificial Intelligence and Statistics, AISTATS 2022 - Virtual, Online, Spain
Duration: Mar 28 2022Mar 30 2022

Conference

Conference25th International Conference on Artificial Intelligence and Statistics, AISTATS 2022
Country/TerritorySpain
CityVirtual, Online
Period03/28/2203/30/22

ASJC Scopus subject areas

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

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