{"title":"Nonconvex Zeroth-Order Stochastic ADMM Methods with Lower Function Query Complexity.","authors":"Feihu Huang, Shangqian Gao, Jian Pei, Heng Huang","doi":"10.1109/TPAMI.2023.3347082","DOIUrl":null,"url":null,"abstract":"<p><p>Zeroth-order (a.k.a, derivative-free) methods are a class of effective optimization methods for solving complex machine learning problems, where gradients of the objective functions are not available or computationally prohibitive. Recently, although many zeroth-order methods have been developed, these approaches still have two main drawbacks: 1) high function query complexity; 2) not being well suitable for solving the problems with complex penalties and constraints. To address these challenging drawbacks, in this paper, we propose a class of faster zeroth-order stochastic alternating direction method of multipliers (ADMM) methods (ZO-SPIDER-ADMM) to solve the nonconvex finite-sum problems with multiple nonsmooth penalties. Moreover, we prove that the ZO-SPIDER-ADMM methods can achieve a lower function query complexity of [Formula: see text] for finding an ϵ-stationary point, which improves the existing best nonconvex zeroth-order ADMM methods by a factor of [Formula: see text], where n and d denote the sample size and data dimension, respectively. At the same time, we propose a class of faster zeroth-order online ADMM methods (ZOO-ADMM+) to solve the nonconvex online problems with multiple nonsmooth penalties. We also prove that the proposed ZOO-ADMM+ methods achieve a lower function query complexity of [Formula: see text], which improves the existing best result by a factor of [Formula: see text]. Extensive experimental results on the structure adversarial attack on black-box deep neural networks demonstrate the efficiency of our new algorithms.</p>","PeriodicalId":94034,"journal":{"name":"IEEE transactions on pattern analysis and machine intelligence","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"IEEE transactions on pattern analysis and machine intelligence","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/TPAMI.2023.3347082","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
Zeroth-order (a.k.a, derivative-free) methods are a class of effective optimization methods for solving complex machine learning problems, where gradients of the objective functions are not available or computationally prohibitive. Recently, although many zeroth-order methods have been developed, these approaches still have two main drawbacks: 1) high function query complexity; 2) not being well suitable for solving the problems with complex penalties and constraints. To address these challenging drawbacks, in this paper, we propose a class of faster zeroth-order stochastic alternating direction method of multipliers (ADMM) methods (ZO-SPIDER-ADMM) to solve the nonconvex finite-sum problems with multiple nonsmooth penalties. Moreover, we prove that the ZO-SPIDER-ADMM methods can achieve a lower function query complexity of [Formula: see text] for finding an ϵ-stationary point, which improves the existing best nonconvex zeroth-order ADMM methods by a factor of [Formula: see text], where n and d denote the sample size and data dimension, respectively. At the same time, we propose a class of faster zeroth-order online ADMM methods (ZOO-ADMM+) to solve the nonconvex online problems with multiple nonsmooth penalties. We also prove that the proposed ZOO-ADMM+ methods achieve a lower function query complexity of [Formula: see text], which improves the existing best result by a factor of [Formula: see text]. Extensive experimental results on the structure adversarial attack on black-box deep neural networks demonstrate the efficiency of our new algorithms.