A Projected Stochastic Gradient Method for Finite-Sum Problems with Linear Equality Constraints

TL;DR

This paper introduces a stochastic gradient method tailored for finite-sum problems with linear equality constraints, extending projected gradient techniques to stochastic and inexact projections, with theoretical analysis and numerical validation.

Contribution

It proposes a novel stochastic projected gradient algorithm for constrained finite-sum problems, incorporating inexact projections and providing theoretical guarantees.

Findings

The method converges under standard stochastic gradient assumptions.

Numerical experiments demonstrate practical effectiveness.

The approach extends classical projected gradient methods to stochastic and inexact settings.

Abstract

A stochastic gradient method for finite-sum minimization subject to deterministic linear constraints is proposed and analyzed. The procedure presented adapts the projected gradient method on convex set to the use of both a stochastic gradient and a possibly inexact projection map. Under standard assumptions in the field of stochastic gradient methods, we provide theoretical results in agreement with the theory for unconstrained problems. Numerical results are presented to show the practical behavior of the procedure.