[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-86113-en":3,"doc-seo-86113-105":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},86113,1374391974468,"Eden","https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0",8,"Research & Report","Regret-weighted Bayes Fusion for Distributed Experimental Design","Distributed experimental design with multiple candidate experiments is studied, where sites hold only partial information and send local design recommendations to a fusion center. The work formulates distributed fusion as a multi-class Bayes decision problem: the centralized oracle choice is treated as an unknown label and each site is modeled by a local recommendation mechanism. A regret-weighted fusion rule minimizes posterior expected information regret, capturing asymmetric losses from choosing incorrect experiments. Majority vote is shown optimal only under restrictive symmetry, and regret-weighted multi-class Chernoff bounds characterize performance separations across regimes. Numerical results compare MAP-leaning behavior to regret-optimized recovery when misalignment occurs.","Regret-weighted Bayes Fusion for Distributed  \nExperimental Design  \nNagananda K G, Lav R. Varshney, Senior Member, IEEE, Pramod K. Varshney, Life Fellow, IEEE  \narXiv :2607 . 11023v1 [math . ST] 13 Jul 2026  \nAbstract—We study distributed experimental design with multiple candidate experiments, where local sites possess only partial information and transmit design recommendations to a fusion center. Unlike centralized design, in which the experiment that maximizes expected information gain can be selected directly, distributed design requires combining heterogeneous and potentially conflicting local recommendations. Formulating as a multi-class Bayes fusion problem, centralized oracle design is treated as an unknown label and each site is characterized by a local recommendation mechanism. The proposed fusion rule minimizes posterior expected information regret, rather than merely maximizing the number of local votes or the posterior probability (MAP) of the oracle label. This distinction is essential because different incorrect experimental choices may incur different losses in information gain. We show that majority vote is optimal only under restrictive symmetry assumptions and can otherwise be strictly suboptimal. Regret-weighted multi-class Chernoff bounds are derived to identify the pairwise separations governing distributed design performance. Numerical studies identify two operational regimes: MAP is effective when oraclelabel accuracy and information regret are aligned, while regretweighted Bayes fusion reduces information loss when the most probable oracle label is not the lowest-regret decision.  \nIndex Terms—distributed Bayesian experimental design; information regret; local recommendation; regret-weighted Bayes fusion; multi-class decision problem.  \nI. INTRODUCTION  \nDistributed experimental design arises when the information needed to select an experiment is dispersed across several sites, agents, sensors, laboratories, clinics, or data repositories [1]–[5] . In a centralized setting, one evaluates the available candidate experiments using a global utility criterion, such as expected information gain (EIG) [6], and selects the experiment that maximizes the criterion. In a distributed setting, however, no single site has access to the full information needed to evaluate the global utility. Each site observes only its own local data structure, population characteristics, measurement constraints, cost profile, or scientific objective; see, e.g., [7]–[13] . Consequently, each site may form a local experiment recommendation that is informative, but incomplete from a global perspective. We focus on the case in which the fusion center must select a common experiment to be implemented  \nNagananda K G is with Fariborz Maseeh Department of Mathematics and Statistics, Portland State University, Portland, OR 97201, USA. (email: [nanda@pdx.edu](nanda@pdx.edu)) .  \nLav R. Varshney is with the AI Innovation Institute, Stony Brook University, Stony Brook, NY 11794, USA, and with Brookhaven National Laboratory, Upton, NY 11973, USA. (email: [lav.varshney@stonybrook.edu](lav.varshney@stonybrook.edu)).  \nPramod K. Varshney is with the Department of Electrical Engineering and Computer Science, Syracuse University, Syracuse, NY 13244 USA. (email: [varshney@syr.edu](varshney@syr.edu)) .  \nacross sites, as occurs when coordinated resource allocation preclude site-specific experimental choices; see, e.g., [14] . The central question is then how to combine these local recommendations into a single global experimental choice that approximates the decision that would have been made under centralized access to all information.  \nA simple approach is to treat the problem as one of voting [15]–[18] . Each site recommends one experiment and the fusion center selects the experiment receiving the most recommendations. Although this approach is easy to implement and appealing in symmetric settings, it ignores several important features of distri","cbCaivl65flqHMv4","https://ap.wps.com/l/cbCaivl65flqHMv4","pdf",374362,4,1,13,"English","en",105,"# Introduction\n## Problem Setup: Distributed vs Centralized Experimental Design\n## Voting Baselines and Their Limitations\n## Binary Formulation and Extension to Multi-class Fusion","[{\"question\":\"How does distributed experimental design differ from centralized experimental design in this paper?\",\"answer\":\"In centralized design, the experiment maximizing expected information gain can be chosen directly because full information is available. In distributed design, no single site has global information, so local recommendations must be combined at a fusion center to approximate the centralized decision.\"},{\"question\":\"What is the key objective optimized by the proposed fusion rule?\",\"answer\":\"The fusion rule minimizes posterior expected information regret rather than maximizing local vote counts or the MAP probability of the oracle label, because different wrong experiment choices can incur different losses in information gain.\"},{\"question\":\"When is majority vote optimal, and why is it otherwise suboptimal?\",\"answer\":\"Majority vote is optimal only under restrictive symmetry assumptions. Otherwise, differences in site reliability and asymmetric consequences of errors make regret-weighted Bayes fusion strictly better.\"}]",1784208596,33,{"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},"regret-weighted-bayes-fusion-for-distributed-experimental-design","",{"@graph":36,"@context":85},[37,53,68],{"@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":20},"https://docshare.wps.com/document/regret-weighted-bayes-fusion-for-distributed-experimental-design/86113/",{"url":52,"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","2026-07-24","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},"How does distributed experimental design differ from centralized experimental design in this paper?","Question",{"text":75,"@type":76},"In centralized design, the experiment maximizing expected information gain can be chosen directly because full information is available. In distributed design, no single site has global information, so local recommendations must be combined at a fusion center to approximate the centralized decision.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"What is the key objective optimized by the proposed fusion rule?",{"text":80,"@type":76},"The fusion rule minimizes posterior expected information regret rather than maximizing local vote counts or the MAP probability of the oracle label, because different wrong experiment choices can incur different losses in information gain.",{"name":82,"@type":73,"acceptedAnswer":83},"When is majority vote optimal, and why is it otherwise suboptimal?",{"text":84,"@type":76},"Majority vote is optimal only under restrictive symmetry assumptions. 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