EG-VSSA: An extragradient variable sample-size stochastic approximation scheme: Error analysis and complexity trade-offs

Afrooz Jalilzadeh, Vinayak V. Shanbhag

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

3 Scopus citations

Abstract

Given a sampling budget M, stochastic approximation (SA) schemes for constrained stochastic convex programs generally utilize a single sample for each projection, requiring an effort ofM projection operations, each of possibly significant complexity. We present an extragradient-based variable sample-size SA scheme (eg-VSSA) that uses Nk samples at step k where ϵk Nk > M. We make the following contributions: (i) In strongly convex regimes, the expected error decays linearly in the number of projection steps; (ii) In convex settings, if the sample-size is increased at suitable rates and the steplength is optimally chosen, the error diminishes at δ(1=K-d1) and δ(1/ √M), requiring O(M1/(2-d2)) steps, where K denotes the number of steps and d1;d2 > 0 can be made arbitrarily small. Preliminary numerics reveal that increasing sample-size schemes provide solutions of similar accuracy to SA schemes but with effort reduced by factors as high as 20.

Original languageEnglish (US)
Title of host publication2016 Winter Simulation Conference
Subtitle of host publicationSimulating Complex Service Systems, WSC 2016
EditorsTheresa M. Roeder, Peter I. Frazier, Robert Szechtman, Enlu Zhou
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages690-701
Number of pages12
ISBN (Electronic)9781509044863
DOIs
StatePublished - Jul 2 2016
Event2016 Winter Simulation Conference, WSC 2016 - Arlington, United States
Duration: Dec 11 2016Dec 14 2016

Publication series

NameProceedings - Winter Simulation Conference
Volume0
ISSN (Print)0891-7736

Other

Other2016 Winter Simulation Conference, WSC 2016
CountryUnited States
CityArlington
Period12/11/1612/14/16

All Science Journal Classification (ASJC) codes

  • Software
  • Modeling and Simulation
  • Computer Science Applications

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    Jalilzadeh, A., & Shanbhag, V. V. (2016). EG-VSSA: An extragradient variable sample-size stochastic approximation scheme: Error analysis and complexity trade-offs. In T. M. Roeder, P. I. Frazier, R. Szechtman, & E. Zhou (Eds.), 2016 Winter Simulation Conference: Simulating Complex Service Systems, WSC 2016 (pp. 690-701). [7822133] (Proceedings - Winter Simulation Conference; Vol. 0). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/WSC.2016.7822133