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The method provides δ-correctness and asymptotic optimality, validated on a large-scale real-world advertising dataset (IPinYou).",{"@graph":14,"@context":73},[15,34,56],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/document/","Document",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/document/research-report/","Research & Report",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/document/fixed-confidence-best-arm-identification-for-causal-mediation-analysis/327906/",4,{"url":32,"name":10,"@type":35,"image":36,"author":41,"headline":10,"publisher":44,"fileFormat":47,"inLanguage":8,"description":12,"dateModified":48,"datePublished":49,"encodingFormat":47,"isAccessibleForFree":50,"interactionStatistic":51},"DigitalDocument",{"url":37,"@type":38,"width":39,"height":40},"https://docshare.wps.com/thumbnails/fixed-confidence-best-arm-identification-for-causal-mediation-analysis/327906.png","ImageObject",300,407,{"name":42,"@type":43},"Miles","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-11-12","2026-09-21",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",12,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69],{"name":60,"@type":61,"acceptedAnswer":62},"What does the NDPO measure in causal mediation analysis?","Question",{"text":63,"@type":64},"NDPO captures the potential outcome of an intervention while excluding the pathway transmitted through the mediator, aligning with the first term of the natural direct effect.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"How is the identification problem formulated in a causal bandit setting?",{"text":68,"@type":64},"Actions correspond to interventions on treatment X, with samples drawn i.i.d. from the interventional distribution P(Z, Y | do(X = x)). The paper derives population-level assumptions for expected NDPO using these interventional distributions.",{"name":70,"@type":61,"acceptedAnswer":71},"What is the main contribution of the proposed algorithm?",{"text":72,"@type":64},"The paper develops a fixed-confidence best-arm identification method (TaS-NDPO) under the Track-and-Stop framework, using a cutting-set approach to solve a semi-infinite optimization problem, and proves δ-correctness and asymptotic optimality.","https://schema.org",{"og:url":32,"og:type":75,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":77,"canonical":32},"index,follow",{"doc_id":79,"site_id":7},327906,1790463819,{"code":4,"msg":82,"data":83},"success",[84,88,92,96,101,106,111,115,120,123,127],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":85,"show_sort_weight":86,"slug":87},"Story & Novel",90,"story-novel",{"id":26,"doc_module":4,"doc_module_name":25,"category_name":89,"show_sort_weight":90,"slug":91},"Literature",80,"literature",{"id":33,"doc_module":4,"doc_module_name":25,"category_name":93,"show_sort_weight":94,"slug":95},"Exam",70,"exam",{"id":97,"doc_module":4,"doc_module_name":25,"category_name":98,"show_sort_weight":99,"slug":100},5,"Comic",60,"comic",{"id":102,"doc_module":4,"doc_module_name":25,"category_name":103,"show_sort_weight":104,"slug":105},6,"Technology",50,"technology",{"id":107,"doc_module":4,"doc_module_name":25,"category_name":108,"show_sort_weight":109,"slug":110},7,"Healthcare",40,"healthcare",{"id":112,"doc_module":4,"doc_module_name":25,"category_name":29,"show_sort_weight":113,"slug":114},8,30,"research-report",{"id":116,"doc_module":4,"doc_module_name":25,"category_name":117,"show_sort_weight":118,"slug":119},9,"Religion & Spirituality",20,"religion-spirituality",{"id":118,"doc_module":4,"doc_module_name":25,"category_name":121,"show_sort_weight":118,"slug":122},"World Cup","world-cup",{"id":124,"doc_module":4,"doc_module_name":25,"category_name":125,"show_sort_weight":124,"slug":126},10,"Lifestyle","lifestyle",{"id":128,"doc_module":4,"doc_module_name":25,"category_name":129,"show_sort_weight":97,"slug":130},19,"General","general",{"code":4,"msg":82,"data":132},{"doc_id":79,"user_id":133,"nickname":42,"user_avatar":134,"doc_module":4,"category_id":112,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":55,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":140,"language":141,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":142,"faqs":143,"seo_title":144,"seo_description":12,"update_tm":145,"read_time":146,"preview_page_count":4},13056703019404,"https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0","Fixed-Confidence Best-Arm Identification for Causal Mediation Analysis  \nHarsh Shrivastava 1 Yuta Kawakami 1 Junpei Komiyama 1,2 Jin Tian 1  \n1Mohamed bin Zayed University of Artificial Intelligence (MBZUAI), Abu Dhabi, UAE  \n2RIKEN AIP, Tokyo, Japan  \narXiv :2607 .04315v1 [ stat .ML] 5 Jul 2026  \nAbstract  \nThis paper studies the problem of identifying the treatment that maximizes the expected natural direct potential outcome (NDPO), which captures the potential outcome of an intervention while excluding the pathway transmitted through a mediator that researchers may wish to remove from evaluation. We first establish population-level identification of the expected NDPO in a causal bandit setting using observable interventional distributions. We then develop a fixed-confidence bestarm identification (BAI) algorithm based on the Track-and-Stop (TaS) framework, employing a cutting-set method to solve the resulting semiinfinite optimization problem. The proposed algorithm achieves sample-efficient identification with a high-probability correctness guarantee. We prove that it satisfies δ-correctness and asymptotic optimality. Finally, we validate the approach through empirical evaluations on a large-scale real-world advertising dataset (IPinYou) .  \n1 INTRODUCTION  \nCausal mediation analysis studies how a treatment (X) influences an outcome (Y ) through different pathways [Sobel, 1982, Baron and Kenny, 1986, Robins and Greenland, 1992, Avin et al., 2005, Pearl, 2009, Imai et al., 2010a] . To elucidate causal mechanisms in nonlinear models, Pearl [2001] introduced path-specific effects, including the expected natural direct effect (NDE) via a mediator (Z), defined as E [Yx,Zx0 ]−E[Yx0 ], where Yx,Zx0 denotes the potential outcome under treatment level x with the mediator set to the value it would attain under a reference level x0 , and Yx0 denotes the potential outcome under treatment level x0. The expected NDE measures the causal effect of a treatment on an outcome that is not mediated through the mediator.  \nIn causal bandit problems, the conventional objective is to maximize the interventional mean under arm (treatment) X = x, i.e., E [Yx] = E [Y |do(X = x)][Lattimore et al., 2016, Lee and Bareinboim, 2018, 2019] . However, the interventional mean aggregates effects along all causal pathways, including mechanisms that the researcher may wish to exclude from evaluation (e.g., unethical factor or positioning bias in advertisements) . To isolate the influence via the direct pathway, this paper studies the problem of identifying the arm that maximizes the expected natural direct potential outcome (NDPO), i.e., E [Yx,Zx0 ], in a causal bandit setting. The NDPO corresponds to the first term of the NDE and is defined via a nested counterfactual.  \nIn a causal bandit setting, actions correspond to interventions on X [Lattimore et al., 2016, Lee and Bareinboim, 2018], and one observes i.i.d. samples from the interventional distribution P (Z, Y |do(X = x)) . The identification results of Pearl [2001] are not directly formulated for this setting. Instead, Pearl [2001] established the identification using P (Yx,z) and P (Zx0 ) . Therefore, we first establish the corresponding identification assumptions of the expected NDPO at the population level using the interventional distribution P (Z, Y |do(X = x)) .  \nMoreover, in the bandit setting, a further objective is to identify the target arm using as few samples as possible while ensuring correctness with high probability. Such a problem has been extensively studied in the fixed-confidence best-arm identification (BAI) framework for multi-armed bandits [Mannor and Tsitsiklis, 2004, Glynn and Juneja, 2004, Audibert and Bubeck, 2010, Jamieson and Nowak, 2014, Garivier and Kaufmann, 2016] .  \nWe subsequently investigate the fixed-confidence BAI problem for identifying the expected NDPO-optimal arm, which maximizes the expected NDPO, leveraging the established population-level identification resul","cbCaib7o44ykyrwN","https://ap.wps.com/l/cbCaib7o44ykyrwN","pdf",567778,27,"English","# Abstract\n# 1 Introduction\n# 2 Notation and Background","[{\"question\":\"What does the NDPO measure in causal mediation analysis?\",\"answer\":\"NDPO captures the potential outcome of an intervention while excluding the pathway transmitted through the mediator, aligning with the first term of the natural direct effect.\"},{\"question\":\"How is the identification problem formulated in a causal bandit setting?\",\"answer\":\"Actions correspond to interventions on treatment X, with samples drawn i.i.d. from the interventional distribution P(Z, Y | do(X = x)). The paper derives population-level assumptions for expected NDPO using these interventional distributions.\"},{\"question\":\"What is the main contribution of the proposed algorithm?\",\"answer\":\"The paper develops a fixed-confidence best-arm identification method (TaS-NDPO) under the Track-and-Stop framework, using a cutting-set approach to solve a semi-infinite optimization problem, and proves δ-correctness and asymptotic optimality.\"}]","Fixed-Confidence Best-Arm Identification for Causal Mediation Analysis | PDF",1789978307,68]