Symmetric confidence regions and confidence intervals for normal map formulations of stochastic variational inequalities

TL;DR

This paper develops a method to construct asymptotically exact confidence regions and intervals for solutions of stochastic variational inequalities using the normal map formulation, based on the asymptotic distribution of sample average approximation solutions.

Contribution

It introduces a novel approach for building confidence regions and intervals for SVI solutions via the normal map formulation, leveraging asymptotic distribution analysis.

Findings

Confidence regions are ellipsoids with high probability.

Method provides asymptotically exact confidence intervals.

Applicable to a broad class of equilibrium problems.

Abstract

Stochastic variational inequalities (SVI) model a large class of equilibrium problems subject to data uncertainty, and are closely related to stochastic optimization problems. The SVI solution is usually estimated by a solution to a sample average approximation (SAA) problem. This paper considers the normal map formulation of an SVI, and proposes a method to build asymptotically exact confidence regions and confidence intervals for the solution of the normal map formulation, based on the asymptotic distribution of SAA solutions. The confidence regions are single ellipsoids with high probability. We also discuss the computation of simultaneous and individual confidence intervals.