Accelerating Stochastic Sequential Quadratic Programming for Equality Constrained Optimization using Predictive Variance Reduction

TL;DR

This paper introduces a stochastic sequential quadratic programming method with predictive variance reduction to efficiently solve equality constrained optimization problems, demonstrating convergence and practical effectiveness in machine learning tasks.

Contribution

It presents a novel variance reduction technique within a stochastic SQP framework for equality constrained optimization, with proven convergence guarantees.

Findings

Convergence of the proposed method to first-order stationarity in expectation.

Effective performance on constrained binary classification problems.

Applicability to both constant and adaptive step size strategies.

Abstract

In this paper, we propose a stochastic method for solving equality constrained optimization problems that utilizes predictive variance reduction. Specifically, we develop a method based on the sequential quadratic programming paradigm that employs variance reduction in the gradient approximations. Under reasonable assumptions, we prove that a measure of first-order stationarity evaluated at the iterates generated by our proposed algorithm converges to zero in expectation from arbitrary starting points, for both constant and adaptive step size strategies. Finally, we demonstrate the practical performance of our proposed algorithm on constrained binary classification problems that arise in machine learning.