[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-84452-en":3,"doc-seo-84452-105":29,"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":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":13,"seo_description":14,"update_tm":27,"read_time":28},84452,1099513958762,"Logic","https://ap-avatar.wpscdn.com/avatar/1000023916a998db790?x-image-process=image/resize,m_fixed,w_180,h_180&k=1782109480056885918",8,"Research & Report","Oracle-Efficient Combinatorial Semi-Bandits","Oracle-Efficient Combinatorial Semi-Bandits studies the combinatorial semi-bandit setting where an agent chooses a subset of base arms and receives individual feedback for each selected arm. The model generalizes multi-armed bandits and applies broadly, yet practical scalability is constrained by expensive combinatorial optimization requiring oracle queries every round. The work introduces oracle-efficient frameworks that reduce oracle calls substantially while preserving tight, gap-free regret guarantees across worst-case linear and broader reward models.","Oracle-Efficient Combinatorial Semi-Bandits  \nJung-hun Kim  \nCREST, ENSAE, IP Paris FairPlay joint team, France [junghun.kim@ensae.fr](junghun.kim@ensae.fr)  \nMilan Vojnovi  \nLondon School of Economics United Kingdom [m.vojnovic@lse.ac.uk](m.vojnovic@lse.ac.uk)  \nMin-hwan Oh  \nSeoul National University South Korea [minoh@snu.ac.kr](minoh@snu.ac.kr)  \narXiv :2510 .21431v2 [ stat .ML] 11 Jul 2026  \nAbstract  \nWe study the combinatorial semi-bandit problem where an agent selects a subset of base arms and receives individual feedback. While this generalizes the classical multi-armed bandit and has broad applicability, its scalability is limited by the high cost of combinatorial optimization, requiring oracle queries at every round.  \nTo tackle this, we propose oracle-efficient frameworks that significantly reduce oracle calls while maintaining tight regret guarantees. For the worst-case linear reworanoiinieu, ouWforilgsphmropedasegcr,evva(ed)dgtiuetealOthgeanolr(g Tragno)-linear) rewards. Overall, our methods reduce oracle usage from linear to (doubly) logarithmic in time, with strong theoretical guarantees.  \n1 Introduction  \nThe combinatorial semi-bandit problem extends the classical multi-armed bandit (MAB) model to settings where an agent selects a subset of base arms (a combinatorial action) and receives individual feedback for each. This general framework captures many real-world scenarios, such as product recommendation, where a set of items is recommended to a user [16]; ad slot allocation, where multiple ads are displayed on a webpage [12]; and network routing, where a path comprising several links is selected in a communication network [27] .  \nDue to its broad applicability, the combinatorial semi-bandit problem has been extensively studied in the literature [5, 7, 18, 9, 22, 32] . However, a central challenge lies in the computational complexity of solving the combinatorial optimization problem, which is often NP-hard. As a result, most existing algorithms assume access to an oracle that returns a solution to the combinatorial problem. These algorithms rely on querying the oracle at every round, leading to excessive oracle usage and substantial computational overhead in practice.  \nIn this work, following the computational complexity notions introduced in Balkanski and Singer [1], Fahrbach et al. [11], we distinguish between two measures of oracle efficiency: adaptivity complexity and query complexity, which are defined later. Our goal is to improve oracle efficiency by substantially reducing the overall oracle adaptivity and query complexities in decision-making over a time horizon T, while maintaining tight gap-free regret guarantees that do not depend on the suboptimality gaps. Our main contributions are summarized below and compared with prior work on gap-free combinatorial semi-bandits in Table 1 .  \n• Oracle-efficient algorithms for worst-case linear rewards: We propose two frameworks that significantly reduce oracle query usage while maintaining tight regret guarantees. Using iadthnoteeracaptumlqviterueyofryanbaeoys,AROmpd ml-CMitytheABbmhndimisnynarOmplrmgfrgtieretm/tedofdba))e,(mhemTeped)r,  \naction. To further improve computational practicality by reducing adaptivity complexity, 39th Conference on Neural Information Processing Systems (NeurIPS 2025) .  \nTable 1: Gap-free regret bounds for combinatorial semi-bandit algorithms.  \nCombinatorial Reward Model  \nAlgorithm  \nRegret  \nAdaptivity Complexity  \nQuery Complexity  \nLinear  \n(Worst-case)  \nCUCB [5]  \nCUCB [18] AROQ-CMAB (our work) SROQ-CMAB (our work)  \n((((dTdTdTdT))))  \nΘ(T) Θ(T)  \nΘ(T) Θ(T)  \nO (d log log( T~~m~~d)) O (d log log( T~~m~~d))  \nΘ(log log T) O (d log log T)  \nLinear (Covariance-dependent)  \nOLS-UCB-C [32] AROQ-C-CMAB (our work)  \nSROQ-C-CMAB (our work)  \n si[d] a∈mAsxi∈a σ2i(a)T! Θ(T)  \n si[d] a∈mAsxi∈a σ2i(a)T! O (d2 log(Tm))  \n sd axA iσ2i(a)T! Θ(log log T)  \nΘ(T)  \nO (d2 log(Tm))  \nO (d2 log log T)  \nGeneral  \nSDCB [4] AROQ-GR-CMAB (our ","cbCairlCuZgBnlYX","https://ap.wps.com/l/cbCairlCuZgBnlYX","pdf",960991,1,36,"English","en",105,"# Introduction\n## Problem setting and motivation\n## Oracle efficiency and main contributions\n# Related Work\n## Foundations\n## Covariance and confidence-ellipsoid approaches","[{\"question\":\"What is the combinatorial semi-bandit problem studied in this work?\",\"answer\":\"The agent selects a subset of base arms as a combinatorial action and receives individual feedback for each selected arm.\"},{\"question\":\"Why is oracle usage a key bottleneck in existing methods?\",\"answer\":\"Most algorithms require solving a combinatorial optimization problem, often NP-hard, so they query an oracle at every round, causing excessive oracle calls and computational overhead.\"},{\"question\":\"How does the proposed approach improve oracle efficiency?\",\"answer\":\"It introduces oracle-efficient frameworks that significantly reduce total oracle adaptivity and query complexity while maintaining tight gap-free regret guarantees, including improvements from linear to (doubly) logarithmic oracle usage in time.\"}]",1784195700,91,{"code":4,"msg":30,"data":31},"ok",{"site_id":24,"language":23,"slug":32,"title":13,"keywords":33,"description":14,"schema_data":34,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":27},"oracle-efficient-combinatorial-semi-bandits","",{"@graph":35,"@context":85},[36,53,68],{"@type":37,"itemListElement":38},"BreadcrumbList",[39,43,47,50],{"item":40,"name":41,"@type":42,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":44,"name":45,"@type":42,"position":46},"https://docshare.wps.com/document/","Document",2,{"item":48,"name":12,"@type":42,"position":49},"https://docshare.wps.com/document/research-report/",3,{"item":51,"name":13,"@type":42,"position":52},"https://docshare.wps.com/document/oracle-efficient-combinatorial-semi-bandits/84452/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":23,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":40,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-17","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 is the combinatorial semi-bandit problem studied in this work?","Question",{"text":75,"@type":76},"The agent selects a subset of base arms as a combinatorial action and receives individual feedback for each selected arm.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"Why is oracle usage a key bottleneck in existing methods?",{"text":80,"@type":76},"Most algorithms require solving a combinatorial optimization problem, often NP-hard, so they query an oracle at every round, causing excessive oracle calls and computational overhead.",{"name":82,"@type":73,"acceptedAnswer":83},"How does the proposed approach improve oracle efficiency?",{"text":84,"@type":76},"It introduces oracle-efficient frameworks that significantly reduce total oracle adaptivity and query complexity while maintaining tight gap-free regret guarantees, including improvements from linear to (doubly) logarithmic oracle usage in time.","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":24},{"code":4,"msg":5,"data":92},[93,97,101,105,110,115,120,123,128,131,135],{"id":20,"doc_module":4,"doc_module_name":45,"category_name":94,"show_sort_weight":95,"slug":96},"Story & Novel",90,"story-novel",{"id":46,"doc_module":4,"doc_module_name":45,"category_name":98,"show_sort_weight":99,"slug":100},"Literature",80,"literature",{"id":52,"doc_module":4,"doc_module_name":45,"category_name":102,"show_sort_weight":103,"slug":104},"Exam",70,"exam",{"id":106,"doc_module":4,"doc_module_name":45,"category_name":107,"show_sort_weight":108,"slug":109},5,"Comic",60,"comic",{"id":111,"doc_module":4,"doc_module_name":45,"category_name":112,"show_sort_weight":113,"slug":114},6,"Technology",50,"technology",{"id":116,"doc_module":4,"doc_module_name":45,"category_name":117,"show_sort_weight":118,"slug":119},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":45,"category_name":12,"show_sort_weight":121,"slug":122},30,"research-report",{"id":124,"doc_module":4,"doc_module_name":45,"category_name":125,"show_sort_weight":126,"slug":127},9,"Religion & Spirituality",20,"religion-spirituality",{"id":126,"doc_module":4,"doc_module_name":45,"category_name":129,"show_sort_weight":126,"slug":130},"World Cup","world-cup",{"id":132,"doc_module":4,"doc_module_name":45,"category_name":133,"show_sort_weight":132,"slug":134},10,"Lifestyle","lifestyle",{"id":136,"doc_module":4,"doc_module_name":45,"category_name":137,"show_sort_weight":106,"slug":138},19,"General","general"]