[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-86575-en":3,"doc-seo-86575-105":30,"detail-sidebar-cat-0-en-105":92},{"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},86575,13056703020460,"Valentina","https://ap-avatar.wpscdn.com/avatar/be000253dac470eee5d?_k=1778207105932848923",8,"Research & Report","Fundamental Limitations of Fixed-Budget Best-Arm Identification","Fixed-budget best-arm identification, also known as ranking and selection, considers allocating a limited sampling budget across multiple arms to identify the arm with the largest unknown mean under noisy feedback. A standard benchmark is the static oracle: a non-adaptive strategy selecting sampling proportions with prior knowledge to maximize the exponential error-decay rate. The result shows no algorithm can uniformly match this benchmark: for any number of arms at least three and any one-parameter natural exponential family reward distributions, some instance forces error decay to be bounded below.","arXiv :2607 . 1 1635v 1 [ cs .LG] 13 Jul 2026  \nFundamental Limitations of Fixed-Budget Best-Arm Identification  \nMotti Goldberger Yale University  \nAbstract. In fixed-budget best-arm identification, also known as ranking and selection, an algorithm has a sampling budget to distribute across 􀀠 arms. Each sample provides noisy feedback about that arm’s mean, and the goal is to identify the arm with the largest mean. A common performance benchmark is the static oracle: a non-adaptive strategy that knows the means in advance and chooses fixed sampling proportions to maximize the exponential decay rate of the probability of incorrect identification. Several adaptive algorithms have been constructed such that their sampling proportions converge to the static oracle proportions. However, it has remained open whether any algorithm could match the static oracle’s error decay rate uniformly across all problem instances. We answer this in the negative. For any 􀀠 ≥ 3 and for rewards drawn from any one-parameter natural exponential family, we show that for any algorithm, there is at least one instance where the error decay rate is at most 􀀐 1 + log8(􀀠~~ ~~) 􀀑 −1 times that of the static oracle. This also answers the open question posed by Qin (2022), showing that fixed-budget best-arm identification does not admit a complexity.  \nKey words: Ranking-and-Selection, Best-Arm Identification, Multi-Armed Bandits  \n1. Introduction  \nBest-arm identification (BAI) in multi-armed bandits is the problem of a decision maker who sequentially collects samples to identify the best arm from a set of alternatives. Each arm generates independent rewards from a distribution with an unknown mean, and the goal is to identify the arm with the largest mean. Also referred to as Ranking-and-Selection, BAI arises in settings such as sequential selection in clinical trials, A/B testing, new product development, and simulation optimization. There are two dominant formulations of BAI. In fixed-confidence identification, algorithms are designed to minimize the expected number of samples required to correctly identify the best arm at a prespecified confidence level. In fixed-budget identification, the total number of samples is fixed in advance, and algorithms are designed to minimize the probability of incorrect identification.  \nA BAI problem is specified by the unknown mean rewards of the alternatives; we call this specification a problem instance. A central goal is to characterize the difficulty of a given problem instance—how‘hard’it is to identify the best arm. For fixed-confidence identification, Garivier and Kaufmann (2016) provide a complete answer in the asymptotic regime. They show that there is an instance-dependent lower bound on the expected number of samples required to achieve a target confidence level, and that a single algorithm (Track-and-Stop) achieves this bound on every instance. When such a lower bound exists, and a single algorithm achieves it uniformly over all instances, we say the problem admits a complexity.  \nThe fixed-budget setting is less understood. Qin (2022) posed the open question of whether fixed-budget BAI has a complexity. Degenne (2023) formalized this question and showed that a complexity does not exist in certain special cases. In this paper, we show the fundamental result that when there are at least three arms with rewards drawn from any one-parameter natural exponential family (NEF), fixed-budget best-arm identification does not admit a complexity.  \n1.1. The Fixed-Budget Setting  \nA problem instance with 􀀠 arms is described by its mean vector 􀁠 = (􀁠 1, . . . , 􀁠 􀀠), where 􀀸 ∗ (􀁠) denotes the (assumed unique) arm with the largest mean reward. An algorithm with fixed budget 􀀩 sequentially collects samples, then selects an arm ˆ􀀸􀀩. On instance 􀁠 , 􀀿 􀁠,􀀩 := P􀁠 􀀀 ˆ􀀸􀀩 ≠ 􀀸 ∗ (􀁠)􀀁 denotes the probability of incorrect identification. The relevant asymptotic performance measure is lim inf 􀀩→∞ 1~~􀀩~~ log 􀀿1􀁠,􀀩 , the exponential decay","cbCaiptWqkIYi5cz","https://ap.wps.com/l/cbCaiptWqkIYi5cz","pdf",282505,5,1,17,"English","en",105,"# Introduction\n## The Fixed-Budget Setting\n## Relation to Ranking and Selection","[{\"question\":\"What is fixed-budget best-arm identification in multi-armed bandits?\",\"answer\":\"It is a sequential decision problem where a sampling budget is fixed in advance and samples are collected to identify the arm with the largest mean based on noisy rewards.\"},{\"question\":\"What does the static oracle benchmark represent?\",\"answer\":\"The static oracle is a non-adaptive strategy that, with knowledge of the arm means, chooses fixed sampling proportions to maximize the exponential decay rate of the probability of incorrect identification.\"},{\"question\":\"What main limitation does the paper prove for fixed-budget best-arm identification?\",\"answer\":\"For at least three arms and rewards from any one-parameter natural exponential family, no algorithm can achieve the static oracle’s error decay rate uniformly across all problem instances.\"}]",1784212725,43,{"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":87,"head_meta":89,"extra_data":91,"updated_unix":28},"fundamental-limitations-of-fixed-budget-best-arm-identification","",{"@graph":36,"@context":86},[37,54,69],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"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":50},"https://docshare.wps.com/document/research-report/",3,{"item":52,"name":13,"@type":43,"position":53},"https://docshare.wps.com/document/fundamental-limitations-of-fixed-budget-best-arm-identification/86575/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":24,"description":14,"dateModified":62,"datePublished":63,"encodingFormat":61,"isAccessibleForFree":64,"interactionStatistic":65},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-07-27","2026-07-16",true,{"@type":66,"interactionType":67,"userInteractionCount":20},"InteractionCounter",{"@type":68},"ViewAction",{"@type":70,"mainEntity":71},"FAQPage",[72,78,82],{"name":73,"@type":74,"acceptedAnswer":75},"What is fixed-budget best-arm identification in multi-armed bandits?","Question",{"text":76,"@type":77},"It is a sequential decision problem where a sampling budget is fixed in advance and samples are collected to identify the arm with the largest mean based on noisy rewards.","Answer",{"name":79,"@type":74,"acceptedAnswer":80},"What does the static oracle benchmark represent?",{"text":81,"@type":77},"The static oracle is a non-adaptive strategy that, with knowledge of the arm means, chooses fixed sampling proportions to maximize the exponential decay rate of the probability of incorrect identification.",{"name":83,"@type":74,"acceptedAnswer":84},"What main limitation does the paper prove for fixed-budget best-arm identification?",{"text":85,"@type":77},"For at least three arms and rewards from any one-parameter natural exponential family, no algorithm can achieve the static oracle’s error decay rate uniformly across all problem 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