On projected stochastic gradient descent algorithm with weighted averaging for least squares regression

Kobi Cohen, Angelia Nedic, R. Srikant

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

Abstract

The problem of least squares regression of a ridimensionai unknown parameter is considered. A stochastic gradient descent based algorithm with weighted iterate-averaging that uses a single pass over the data is studied and its convergence rate is analyzed. We first consider a bounded constraint set of the unknown parameter. Under some standard regularity assumptions, we provide an explicit O(1/k) upper bound on the convergence rate, depending on the variance (due to the additive noise in the measurements) and the size of the constraint set. We show that the variance term dominates the error and decreases with rate 1 /k, while the constraint set term decreases with rate log k/k2. We then compare the asymptotic ratio ρ between the convergence rate of the proposed scheme and the empirical risk minimizer (ERM) as the number of iterations approaches infinity. We show that ρ 1. We further improve the upper bound by showing that ρ < 4/3 for the case of d =1 and unbounded parameter set. Simulation results demonstrate strong performance of the algorithm as compared to existing methods, and coincide with ρ < 4/3 even for large d in practice.

Original languageEnglish (US)
Title of host publication2016 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2016 - Proceedings
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages2314-2318
Number of pages5
ISBN (Electronic)9781479999880
DOIs
StatePublished - May 18 2016
Event41st IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2016 - Shanghai, China
Duration: Mar 20 2016Mar 25 2016

Publication series

NameICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
Volume2016-May
ISSN (Print)1520-6149

Other

Other41st IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2016
CountryChina
CityShanghai
Period3/20/163/25/16

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Keywords

  • Convex optimization
  • empirical risk mini-mizer
  • projected stochastic gradient descent
  • weighted averaging

ASJC Scopus subject areas

  • Software
  • Signal Processing
  • Electrical and Electronic Engineering

Cite this

Cohen, K., Nedic, A., & Srikant, R. (2016). On projected stochastic gradient descent algorithm with weighted averaging for least squares regression. In 2016 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2016 - Proceedings (pp. 2314-2318). [7472090] (ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings; Vol. 2016-May). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ICASSP.2016.7472090