A Proximal-Point Algorithm with Variable Sample-Sizes (PPAWSS) for Monotone Stochastic Variational Inequality Problems

Afrooz Jalilzadeh, Uday V. Shanbhag

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

Abstract

We consider a stochastic variational inequality (SVI) problem with a continuous and monotone mapping over a closed and convex set. In strongly monotone regimes, we present a variable sample-size averaging scheme (VS-Ave) that achieves a linear rate with an optimal oracle complexity. In addition, the iteration complexity is shown to display a muted dependence on the condition number compared with standard variance-reduced projection schemes. To contend with merely monotone maps, we develop amongst the first proximal-point algorithms with variable sample-sizes (PPAWSS), where increasingly accurate solutions of strongly monotone SVIs are obtained via (VS-Ave) at every step. This allows for achieving a sublinear convergence rate that matches that obtained for deterministic monotone VIs. Preliminary numerical evidence suggests that the schemes compares well with competing schemes.

Original languageEnglish (US)
Title of host publication2019 Winter Simulation Conference, WSC 2019
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages3551-3562
Number of pages12
ISBN (Electronic)9781728132839
DOIs
StatePublished - Dec 2019
Event2019 Winter Simulation Conference, WSC 2019 - National Harbor, United States
Duration: Dec 8 2019Dec 11 2019

Publication series

NameProceedings - Winter Simulation Conference
Volume2019-December
ISSN (Print)0891-7736

Conference

Conference2019 Winter Simulation Conference, WSC 2019
CountryUnited States
CityNational Harbor
Period12/8/1912/11/19

All Science Journal Classification (ASJC) codes

  • Software
  • Modeling and Simulation
  • Computer Science Applications

Fingerprint Dive into the research topics of 'A Proximal-Point Algorithm with Variable Sample-Sizes (PPAWSS) for Monotone Stochastic Variational Inequality Problems'. Together they form a unique fingerprint.

  • Cite this

    Jalilzadeh, A., & Shanbhag, U. V. (2019). A Proximal-Point Algorithm with Variable Sample-Sizes (PPAWSS) for Monotone Stochastic Variational Inequality Problems. In 2019 Winter Simulation Conference, WSC 2019 (pp. 3551-3562). [9004836] (Proceedings - Winter Simulation Conference; Vol. 2019-December). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/WSC40007.2019.9004836