{"title":"随机累积约束条件下的在线弱 DR 次模块优化","authors":"Junkai Feng;Ruiqi Yang;Yapu Zhang;Zhenning Zhang","doi":"10.26599/TST.2023.9010039","DOIUrl":null,"url":null,"abstract":"In this paper, we study a class of online continuous optimization problems. At each round, the utility function is the sum of a weakly diminishing-returns (DR) submodular function and a concave function, certain cost associated with the action will occur, and the problem has total limited budget. Combining the two methods, the penalty function and Frank-Wolfe strategies, we present an online method to solve the considered problem. Choosing appropriate stepsize and penalty parameters, the performance of the online algorithm is guaranteed, that is, it achieves sub-linear regret bound and certain mild constraint violation bound in expectation.","PeriodicalId":48690,"journal":{"name":"Tsinghua Science and Technology","volume":null,"pages":null},"PeriodicalIF":6.6000,"publicationDate":"2024-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=10433470","citationCount":"0","resultStr":"{\"title\":\"Online Weakly DR-Submodular Optimization Under Stochastic Cumulative Constraints\",\"authors\":\"Junkai Feng;Ruiqi Yang;Yapu Zhang;Zhenning Zhang\",\"doi\":\"10.26599/TST.2023.9010039\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we study a class of online continuous optimization problems. At each round, the utility function is the sum of a weakly diminishing-returns (DR) submodular function and a concave function, certain cost associated with the action will occur, and the problem has total limited budget. Combining the two methods, the penalty function and Frank-Wolfe strategies, we present an online method to solve the considered problem. Choosing appropriate stepsize and penalty parameters, the performance of the online algorithm is guaranteed, that is, it achieves sub-linear regret bound and certain mild constraint violation bound in expectation.\",\"PeriodicalId\":48690,\"journal\":{\"name\":\"Tsinghua Science and Technology\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":6.6000,\"publicationDate\":\"2024-02-12\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=10433470\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Tsinghua Science and Technology\",\"FirstCategoryId\":\"94\",\"ListUrlMain\":\"https://ieeexplore.ieee.org/document/10433470/\",\"RegionNum\":1,\"RegionCategory\":\"计算机科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"Multidisciplinary\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Tsinghua Science and Technology","FirstCategoryId":"94","ListUrlMain":"https://ieeexplore.ieee.org/document/10433470/","RegionNum":1,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Multidisciplinary","Score":null,"Total":0}
Online Weakly DR-Submodular Optimization Under Stochastic Cumulative Constraints
In this paper, we study a class of online continuous optimization problems. At each round, the utility function is the sum of a weakly diminishing-returns (DR) submodular function and a concave function, certain cost associated with the action will occur, and the problem has total limited budget. Combining the two methods, the penalty function and Frank-Wolfe strategies, we present an online method to solve the considered problem. Choosing appropriate stepsize and penalty parameters, the performance of the online algorithm is guaranteed, that is, it achieves sub-linear regret bound and certain mild constraint violation bound in expectation.
期刊介绍:
Tsinghua Science and Technology (Tsinghua Sci Technol) started publication in 1996. It is an international academic journal sponsored by Tsinghua University and is published bimonthly. This journal aims at presenting the up-to-date scientific achievements in computer science, electronic engineering, and other IT fields. Contributions all over the world are welcome.