TY - GEN
T1 - A Proximal-Point Algorithm with Variable Sample-Sizes (PPAWSS) for Monotone Stochastic Variational Inequality Problems
AU - Jalilzadeh, Afrooz
AU - Shanbhag, Uday V.
N1 - Publisher Copyright:
© 2019 IEEE.
PY - 2019/12
Y1 - 2019/12
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85081121405&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85081121405&partnerID=8YFLogxK
U2 - 10.1109/WSC40007.2019.9004836
DO - 10.1109/WSC40007.2019.9004836
M3 - Conference contribution
AN - SCOPUS:85081121405
T3 - Proceedings - Winter Simulation Conference
SP - 3551
EP - 3562
BT - 2019 Winter Simulation Conference, WSC 2019
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2019 Winter Simulation Conference, WSC 2019
Y2 - 8 December 2019 through 11 December 2019
ER -