An Inexact Variance-Reduced Method For Stochastic Quasi-Variational Inequality Problems With An Application In Healthcare

TL;DR

This paper introduces an inexact variance-reduced stochastic method for solving complex stochastic quasi-variational inequality problems, with applications in healthcare, demonstrating linear convergence and practical modeling of blood donation competition.

Contribution

It proposes a novel inexact variance-reduced algorithm for SQVI problems with convergence analysis and applies it to model healthcare-related competition scenarios.

Findings

Achieves linear convergence rate with increasing sample size

Models blood donation competition as an SQVI problem

Provides preliminary simulation results validating the approach

Abstract

This paper is focused on a stochastic quasi-variational inequality (SQVI) problem with a continuous and strongly-monotone mapping over a closed and convex set where the projection onto the constraint set may not be easy to compute. We present an inexact variance reduced stochastic scheme to solve SQVI problems and analyzed its convergence rate and oracle complexity. A linear rate of convergence is obtained by progressively increasing sample-size and approximating the projection operator. Moreover, we show how a competition among blood donation organizations can be modeled as an SQVI and we provide some preliminary simulation results to validate our findings.