{"title":"Optimality Gap of Decentralized Submodular Maximization under Probabilistic Communication","authors":"Joan Vendrell, Solmaz Kia","doi":"arxiv-2409.09979","DOIUrl":null,"url":null,"abstract":"This paper considers the problem of decentralized submodular maximization\nsubject to partition matroid constraint using a sequential greedy algorithm\nwith probabilistic inter-agent message-passing. We propose a\ncommunication-aware framework where the probability of successful communication\nbetween connected devices is considered. Our analysis introduces the notion of\nthe probabilistic optimality gap, highlighting its potential influence on\ndetermining the message-passing sequence based on the agent's broadcast\nreliability and strategic decisions regarding agents that can broadcast their\nmessages multiple times in a resource-limited environment. This work not only\ncontributes theoretical insights but also has practical implications for\ndesigning and analyzing decentralized systems in uncertain communication\nenvironments. A numerical example demonstrates the impact of our results.","PeriodicalId":501245,"journal":{"name":"arXiv - MATH - Probability","volume":"122 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Probability","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.09979","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
This paper considers the problem of decentralized submodular maximization
subject to partition matroid constraint using a sequential greedy algorithm
with probabilistic inter-agent message-passing. We propose a
communication-aware framework where the probability of successful communication
between connected devices is considered. Our analysis introduces the notion of
the probabilistic optimality gap, highlighting its potential influence on
determining the message-passing sequence based on the agent's broadcast
reliability and strategic decisions regarding agents that can broadcast their
messages multiple times in a resource-limited environment. This work not only
contributes theoretical insights but also has practical implications for
designing and analyzing decentralized systems in uncertain communication
environments. A numerical example demonstrates the impact of our results.