论文标题
一种自适应采样顺序二次编程方法，用于平等约束随机优化
An Adaptive Sampling Sequential Quadratic Programming Method for Equality Constrained Stochastic Optimization
论文作者
论文摘要
本文提出了一种在顺序二次编程（SQP）方法中使用不同样本大小的方法来解决平等约束的随机优化问题。本文的第一部分介绍了在评估梯度以及对SQP子问题的不精确解决方案时，介绍了动态样本选择的精致问题。在合理的假设上，对所采用梯度近似值的质量以及对SQP子问题的解决方案的准确性，我们为所提出的方法建立了全局收敛结果。本文的第二部分是由这些结果激励的，描述了一种实用的自适应不进行随机顺序二次编程（PAIS-SQP）方法。我们提出了基于在优化过程中获得的随机梯度近似值的方差估计的估计，以控制SQP子问题的样本量和准确性的标准。最后，我们在可爱的问题和受约束分类任务的子集上演示了实用方法的性能。
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.
