RSN: Randomized subspace Newton

Robert M. Gower, Felix Lieder, Dmitry Kovalev, Peter Richtárik

Research output: Contribution to conferencePaperpeer-review

29 Scopus citations


We develop a randomized Newton method capable of solving learning problems with huge dimensional feature spaces, which is a common setting in applications such as medical imaging, genomics and seismology. Our method leverages randomized sketching in a new way, by finding the Newton direction constrained to the space spanned by a random sketch. We develop a simple global linear convergence theory that holds for practically all sketching techniques, which gives the practitioners the freedom to design custom sketching approaches suitable for particular applications. We perform numerical experiments which demonstrate the efficiency of our method as compared to accelerated gradient descent and the full Newton method. Our method can be seen as a refinement and randomized extension of the results of Karimireddy, Stich, and Jaggi [18].

Original languageEnglish (US)
StatePublished - 2019
Event33rd Annual Conference on Neural Information Processing Systems, NeurIPS 2019 - Vancouver, Canada
Duration: Dec 8 2019Dec 14 2019


Conference33rd Annual Conference on Neural Information Processing Systems, NeurIPS 2019

Bibliographical note

Publisher Copyright:
© 2019 Neural information processing systems foundation. All rights reserved.

ASJC Scopus subject areas

  • Computer Networks and Communications
  • Information Systems
  • Signal Processing


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