A Proximal-Point Algorithm with Variable Sample-sizes (PPAWSS) for Monotone Stochastic Variational Inequality Problems
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.
Cite
@article{arxiv.1909.13424,
title = {A Proximal-Point Algorithm with Variable Sample-sizes (PPAWSS) for Monotone Stochastic Variational Inequality Problems},
author = {Afrooz Jalilzadeh and Uday V. Shanbhag},
journal= {arXiv preprint arXiv:1909.13424},
year = {2019}
}