Gradient-Free Algorithms for Solving Stochastic Saddle Optimization Problems with the Polyak–Łojasiewicz Condition

IF 0.7 4区计算机科学 Q4 COMPUTER SCIENCE, SOFTWARE ENGINEERING

Programming and Computer Software Pub Date : 2023-12-01 DOI:10.1134/s0361768823060063

S. I. Sadykov, A. V. Lobanov, A. M. Raigorodskii

引用次数: 0

Abstract

This paper focuses on solving a subclass of stochastic nonconvex-nonconcave black box optimization problems with a saddle point that satisfy the Polyak–Łojasiewicz (PL) condition. To solve this problem, we provide the first (to our best knowledge) gradient-free algorithm. The proposed approach is based on applying a gradient approximation (kernel approximation) to an oracle-biased stochastic gradient descent algorithm. We present theoretical estimates that guarantee its global linear rate of convergence to the desired accuracy. The theoretical results are checked on a model example by comparison with an algorithm using Gaussian approximation.

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求解Polyak -Łojasiewicz条件下随机鞍型优化问题的无梯度算法

摘要研究了一类鞍点满足Polyak -Łojasiewicz (PL)条件的随机非凸非凹黑箱优化问题。为了解决这个问题，我们提供了第一个(据我们所知)无梯度算法。该方法基于将梯度近似(核近似)应用于oracle-biased stochastic gradient descent算法。我们给出了保证其全局线性收敛速度达到期望精度的理论估计。通过与高斯近似算法的比较，验证了理论结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Programming and Computer Software 工程技术-计算机：软件工程

CiteScore

1.60

自引率

28.60%

发文量

审稿时长

>12 weeks

期刊介绍： Programming and Computer Software is a peer reviewed journal devoted to problems in all areas of computer science: operating systems, compiler technology, software engineering, artificial intelligence, etc.