An Adaptive Sampling Sequential Quadratic Programming Method for Equality Constrained Stochastic Optimization

TL;DR

This paper introduces an adaptive sampling approach for stochastic SQP methods that dynamically adjusts sample sizes and solution accuracy, ensuring convergence and improving efficiency in equality constrained stochastic optimization.

Contribution

It develops a practical adaptive inexact stochastic SQP method with criteria for sample size and accuracy control, validated on benchmark problems.

Findings

Global convergence under reasonable assumptions

Effective sample size and accuracy control criteria

Demonstrated improved performance on benchmark problems

Abstract

This paper presents a methodology for using varying sample sizes in sequential quadratic programming (SQP) methods for solving equality constrained stochastic optimization problems. The first part of the paper deals with the delicate issue of dynamic sample selection in the evaluation of the gradient in conjunction with inexact solutions to the SQP subproblems. Under reasonable assumptions on the quality of the employed gradient approximations and the accuracy of the solutions to the SQP subproblems, we establish global convergence results for the proposed method. Motivated by these results, the second part of the paper describes a practical adaptive inexact stochastic sequential quadratic programming (PAIS-SQP) method. We propose criteria for controlling the sample size and the accuracy in the solutions of the SQP subproblems based on estimates of the variance in the stochastic gradient approximations obtained as the optimization progresses. Finally, we demonstrate the performance of the practical method on a subset of the CUTE problems and constrained classification tasks.