[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-84586-en":3,"doc-seo-84586-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":13,"seo_description":14,"update_tm":28,"read_time":29},84586,16904993612988,"Olivia Brown","https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd",8,"Research & Report","Distributed Online Bandit Submodular Maximization with Bounded Sampling Violations","Distributed online submodular maximization is studied under partition matroid constraints, where multiple agents sequentially choose a limited number of actions from their local sets to maximize the cumulative value over time-varying objective functions. A unified algorithmic framework is proposed for both full-information and bandit feedback. For each feedback model, sublinear regret with a (1 − 1/e) benchmark is proven and shown to match centralized baselines. Sampling violation from relaxation and rounding is handled via bounded stochastic pipage rounding, yielding asymptotically vanishing violation probability and sublinear total violation, supported by numerical experiments.","arXiv :2607 .00680v 1 [ cs .LG] 1 Jul 2026  \nDistributed Online Bandit Submodular Maximization with Bounded Sampling Violations  \nBin Du ∗ Chang Liu∗ Dingqi Zhu∗ Lintao Ye† Dengfeng Sun‡  \nJuly 2, 2026  \nAbstract  \nWe study distributed online submodular maximization under partition matroid constraints, in which multiple agents select a limited number of actions from their own subsets sequentially to maximize the cumulative value of a sequence of objective functions. We develop a unified algorithmic framework that accommodates full-information and bandit feedback models. For both feedback models, we prove that the proposed algorithms achieve sublinear (1 − 1/e)-regret guarantees, which are comparable to those achieved by existing centralized counterparts. Furthermore, to tackle the sampling violation issue caused by continuous relaxation and rounding, we develop a bounded stochastic pipage rounding scheme and show that the probability of sampling violation vanishes asymptotically. As a result, the cumulative sampling violation remains sublinear in T , which is further shown to be not improvable under certain conditions. Numerical results validate the theoretical findings in this paper.  \n1 Introduction  \nSubmodular maximization is a fundamental problem in a broad range of applications such as sensorselection [1], resource allocation [2], and task coordination with multi-agent systems [3] . In its general form, the problem aims to maximize a set function subject to certain combinatorial constraints, such as cardinality or matroid constraints. Despite its applicability, this class of problems is known to be NP-hard [4] and hence its exact solutions are computationally intractable in general. As a consequence, a substantial body of research has focused on the development of efficient approximation algorithms with provable performance guarantees. A rich line of such work has established that constant-factor approximation ratios, e.g. , 1/2 or 1 − 1/e, can be achieved via greedy-based methods or their continuous variants [5–7] . Additionally, these guarantees are further shown to be optimal unless P = NP [4] . Such a result has provided a solid theoretical foundation for designing algorithms that achieve near-optimal performance guarantees while remaining computationally tractable.  \nBeyond the classical centralized problem, there has been a growing interest in studying distributed submodular maximization, see e.g., [8–11], motivated by large-scale decision-making scenarios over multi-agent networks. One typical class of distributed problems arises when agents possess distributed  \n∗ College of Automation Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China;{iniesdu, liuch, [zdq.bpz}@nuaa.edu.cn](zdq.bpz}@nuaa.edu.cn)  \n†School of Artificial Intelligence and Automation at the Huazhong University of Science and Technology, Wuhan, China; [yelintao93@hust.edu.cn](yelintao93@hust.edu.cn)  \n‡School of Aeronautics and Astronautics, Purdue University, West Lafayette, IN 47906, USA; [dsun@purdue.edu](dsun@purdue.edu)  \naction subsets, and feasibility is enforced through combinatorial constraints coupling all agents’decisions, e.g., [11, 12] . A canonical example is the partition matroid constraint [13], where the ground action set is partitioned over multiple agents and each one is allowed to select one or a few actions only from its local set. To solve the distributed submodular maximization under such constraints, the authors in [12] propose a solution method that combines the classical continuous greedy algorithm (also known as the Frank-Wolfe algorithm) with the consensus-based coordination scheme. However, this method relies on the exact gradient evaluation of the multi-linear extension of the submodular objective function, leading to computational complexity that grows exponentially with the size of the action set. To address this issue, the authors in [13] develop a distributed algorithm by following","cbCait9kpbJhpgSD","https://ap.wps.com/l/cbCait9kpbJhpgSD","pdf",2210689,3,1,34,"English","en",105,"# Introduction\n## Distributed submodular maximization\n## Online submodular maximization\n## Related approaches and challenges","[{\"question\":\"What problem does the paper address?\",\"answer\":\"The paper studies distributed online submodular maximization where multiple agents select limited actions sequentially under partition matroid constraints to maximize cumulative objective value.\"},{\"question\":\"How does the proposed framework handle different feedback settings?\",\"answer\":\"It provides a unified algorithmic framework that works under both full-information and bandit feedback models, proving comparable regret guarantees in each case.\"},{\"question\":\"What is the sampling violation issue and how is it mitigated?\",\"answer\":\"Sampling violation can arise from continuous relaxation and rounding. The paper introduces a bounded stochastic pipage rounding scheme that makes the probability of violation vanish asymptotically, keeping cumulative sampling violation sublinear in T.\"}]",1784196954,86,{"code":4,"msg":31,"data":32},"ok",{"site_id":25,"language":24,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"distributed-online-bandit-submodular-maximization-with-bounded-sampling-violations","",{"@graph":36,"@context":85},[37,53,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,50],{"item":41,"name":42,"@type":43,"position":21},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":20},"https://docshare.wps.com/document/research-report/",{"item":51,"name":13,"@type":43,"position":52},"https://docshare.wps.com/document/distributed-online-bandit-submodular-maximization-with-bounded-sampling-violations/84586/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":24,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":41,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-21","2026-07-16",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What problem does the paper address?","Question",{"text":75,"@type":76},"The paper studies distributed online submodular maximization where multiple agents select limited actions sequentially under partition matroid constraints to maximize cumulative objective value.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does the proposed framework handle different feedback settings?",{"text":80,"@type":76},"It provides a unified algorithmic framework that works under both full-information and bandit feedback models, proving comparable regret guarantees in each case.",{"name":82,"@type":73,"acceptedAnswer":83},"What is the sampling violation issue and how is it mitigated?",{"text":84,"@type":76},"Sampling violation can arise from continuous relaxation and rounding. The paper introduces a bounded stochastic pipage rounding scheme that makes the probability of violation vanish asymptotically, keeping cumulative sampling violation sublinear in T.","https://schema.org",{"og:url":51,"og:type":87,"og:title":13,"og:site_name":58,"og:description":14},"article",{"robots":89,"canonical":51},"index,follow",{"doc_id":7,"site_id":25},{"code":4,"msg":5,"data":92},[93,97,101,105,110,115,120,123,128,131,135],{"id":21,"doc_module":4,"doc_module_name":46,"category_name":94,"show_sort_weight":95,"slug":96},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":98,"show_sort_weight":99,"slug":100},"Literature",80,"literature",{"id":52,"doc_module":4,"doc_module_name":46,"category_name":102,"show_sort_weight":103,"slug":104},"Exam",70,"exam",{"id":106,"doc_module":4,"doc_module_name":46,"category_name":107,"show_sort_weight":108,"slug":109},5,"Comic",60,"comic",{"id":111,"doc_module":4,"doc_module_name":46,"category_name":112,"show_sort_weight":113,"slug":114},6,"Technology",50,"technology",{"id":116,"doc_module":4,"doc_module_name":46,"category_name":117,"show_sort_weight":118,"slug":119},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":121,"slug":122},30,"research-report",{"id":124,"doc_module":4,"doc_module_name":46,"category_name":125,"show_sort_weight":126,"slug":127},9,"Religion & Spirituality",20,"religion-spirituality",{"id":126,"doc_module":4,"doc_module_name":46,"category_name":129,"show_sort_weight":126,"slug":130},"World Cup","world-cup",{"id":132,"doc_module":4,"doc_module_name":46,"category_name":133,"show_sort_weight":132,"slug":134},10,"Lifestyle","lifestyle",{"id":136,"doc_module":4,"doc_module_name":46,"category_name":137,"show_sort_weight":106,"slug":138},19,"General","general"]