{"title":"用于在线复合优化的在线主要半近似 ADMM 的遗憾分析","authors":"Zehao Xiao, Liwei Zhang","doi":"10.1007/s10898-024-01365-5","DOIUrl":null,"url":null,"abstract":"<p>An online majorized semi-proximal alternating direction method of multiplier (Online-mspADMM) is proposed for a broad class of online linearly constrained composite optimization problems. A majorized technique is adopted to produce subproblems which can be easily solved. Under mild assumptions, we establish <span>\\(\\mathcal {O}(\\sqrt{N})\\)</span> objective regret and <span>\\(\\mathcal {O}(\\sqrt{N})\\)</span> constraint violation regret at round <i>N</i>. We apply the Online-mspADMM to solve different types of online regularized logistic regression problems. The numerical results on synthetic data sets verify the theoretical result about regrets.</p>","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Regret analysis of an online majorized semi-proximal ADMM for online composite optimization\",\"authors\":\"Zehao Xiao, Liwei Zhang\",\"doi\":\"10.1007/s10898-024-01365-5\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>An online majorized semi-proximal alternating direction method of multiplier (Online-mspADMM) is proposed for a broad class of online linearly constrained composite optimization problems. A majorized technique is adopted to produce subproblems which can be easily solved. Under mild assumptions, we establish <span>\\\\(\\\\mathcal {O}(\\\\sqrt{N})\\\\)</span> objective regret and <span>\\\\(\\\\mathcal {O}(\\\\sqrt{N})\\\\)</span> constraint violation regret at round <i>N</i>. We apply the Online-mspADMM to solve different types of online regularized logistic regression problems. The numerical results on synthetic data sets verify the theoretical result about regrets.</p>\",\"PeriodicalId\":1,\"journal\":{\"name\":\"Accounts of Chemical Research\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":16.4000,\"publicationDate\":\"2024-02-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Accounts of Chemical Research\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s10898-024-01365-5\",\"RegionNum\":1,\"RegionCategory\":\"化学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"CHEMISTRY, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s10898-024-01365-5","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
摘要
针对各类在线线性约束复合优化问题，提出了一种在线大化半近似交替方向乘法（Online-mspADMM）。该方法采用大化技术来生成易于求解的子问题。在温和的假设条件下，我们在第 N 轮建立了 \(\mathcal {O}(\sqrt{N})\) 目标遗憾和 \(\mathcal {O}(\sqrt{N})\) 约束违反遗憾。在合成数据集上的数值结果验证了关于遗憾的理论结果。
Regret analysis of an online majorized semi-proximal ADMM for online composite optimization
An online majorized semi-proximal alternating direction method of multiplier (Online-mspADMM) is proposed for a broad class of online linearly constrained composite optimization problems. A majorized technique is adopted to produce subproblems which can be easily solved. Under mild assumptions, we establish \(\mathcal {O}(\sqrt{N})\) objective regret and \(\mathcal {O}(\sqrt{N})\) constraint violation regret at round N. We apply the Online-mspADMM to solve different types of online regularized logistic regression problems. The numerical results on synthetic data sets verify the theoretical result about regrets.
期刊介绍：
Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance.
Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.
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