[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-84859-en":3,"doc-seo-84859-105":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},84859,8796095461564,"Liam","https://ap-avatar.wpscdn.com/davatar_155a257f0dc6eb9ab79c44ca47cae57d",8,"Research & Report","Contextual Procurement Auctions with Bandit Learning","Repeated contextual procurement auctions are studied where producers hold private costs and a platform must learn context-dependent product values using bandit feedback. The objective is welfare, not revenue, measured by welfare regret as total surplus loss relative to the full-information efficient procurement rule. An initial UCB allocation yields eO(√n g T) welfare regret under truthful bids, but adaptive learning alone fails to guarantee truthfulness. A bid-independent explore-then-commit design with empirical critical payments is dominant-strategy truthful with eO((ng)1/3 T2/3) regret. Frozen-payment UCB estimates payments in an initial exploration phase, freezes them, and continues UCB allocation learning, achieving optimal regret tradeoffs and a matching lower bound.","Contextual Procurement Auctions with Bandit Learning  \nYiling Chen∗ , Shi Feng, and Sadie Zhao  \nHarvard University  \n[yiling@seas.harvard.edu](yiling@seas.harvard.edu), [shifeng-thu@outlook.com](shifeng-thu@outlook.com), [sadie_zhao@g.harvard.edu](sadie_zhao@g.harvard.edu)  \narXiv :2607 .058 13v2 [ cs .GT] 8 Jul 2026  \nAbstract  \nWe study repeated contextual procurement auctions in which producers have private costs and the platform must learn context-dependent product values from bandit feedback. The objective is welfare rather than revenue or a virtual-cost surrogate: regret is the total surplus loss relative to the fullinformation efficient procurement rule. We first show that the natural UCB allocation rule attains eO( √ngT) welfare regret under truthful bids, but its adaptive bid-dependent learning path does not by itself give a truthfulness guarantee. To obtain exact incentives, we design a bid-independent explorethen-commit mechanism with empirical critical payments; it is dominant-strategy truthful and has eO((ng)1/3T2/3) regret. We then introduce frozen-payment UCB, which estimates payments in an initial bid-independent exploration phase, freezes those payment estimates, and continues adaptive UCB allocation learning afterwards. Under a smoothed truthful-path margin condition, this mechanism gives a regret-incentive tradeoff: the near-UCB tuning attains eO( √ngT) welfare regret, while the average per-round gain from any fixed deviation is at most eO(T−1/4) for fixed n, g. A matching lower bound shows that this frozen-payment frontier is unavoidable.  \nIntroduction  \nAuctions are often used not merely to extract revenue, but to allocate scarce resources whose productive value is initially uncertain (Vickrey 1961); see also the standard auctiontheory treatments of Milgrom (Milgrom 2004) and Krishna (Krishna 2009) . A useful historical example is the leasing of the Laurion silver mines in classical Athens. The surviving Athenian records document leases and public sales administered by the poletai, the official sellers, and modern studies of these inscriptions show that the leased mines varied by location, history, classification, and price (Crosby 1950; Lalonde, Langdon, and Walbank 1991; Aperghis 1998) . From a modern allocation perspective, a mining lease was not a known object with a fixed value. Its realized value depended on geological conditions, prior excavation, nearby discoveries, extraction technology, operating costs, and the state of silver demand. Selling a lease to the highest bidder could raise public revenue, but it need not allocate the right to the operator who would generate the greatest total surplus.  \n∗Authors are listed alphabetically by last name.  \nThis example suggests a counterfactual design question that is still central today: how should a public operator allocate resources when the welfare contribution of each allocation is context-dependent and must be learned over time? A modern mechanism could deliberately explore undersampled mine categories, use realized production as bandit feedback about productivity, and then allocate future rights using estimates of surplus rather than payments alone. The loss from early mistakes would be measured not only by foregone lease revenue, but by the cumulative social value lost from allocating public assets without knowing which operator can use them best. This is the lens of welfare regret: the gap between the welfare achieved by an online mechanism and the welfare that would have been achieved by an oracle that knew the true context-value relationship.  \nThe same structure appears in contemporary infrastructure markets. Electricity markets are the leading example. System operators repeatedly procure and dispatch generation, storage, and demand response under contexts such as seasonality, weather, renewable output, fuel prices, congestion, and industrial load. The canonical spot-pricing and network-pricing literature treats efficient dispatch as an opti","cbCaibVTiKDQc8Li","https://ap.wps.com/l/cbCaibVTiKDQc8Li","pdf",445229,1,14,"English","en",105,"# Abstract\n# Introduction\n## Motivating examples and welfare-coordination motivation\n## Problem formulation and full-information benchmark","[{\"question\":\"What is the welfare goal in these contextual procurement auctions?\",\"answer\":\"The mechanism targets welfare rather than revenue. Welfare regret is defined as the total surplus loss relative to the full-information efficient procurement rule.\"},{\"question\":\"Why doesn’t the natural UCB allocation rule automatically ensure truthful bidding?\",\"answer\":\"Although the UCB rule achieves welfare regret under truthful bids, its adaptive bid-dependent learning path does not provide a truthfulness guarantee by itself.\"},{\"question\":\"How do the proposed incentive mechanisms achieve truthfulness and low regret?\",\"answer\":\"The explore-then-commit mechanism uses bid-independent exploration and empirical critical payments to be dominant-strategy truthful. The frozen-payment UCB further freezes estimated payments after an initial exploration, enabling a tuned regret–incentive tradeoff that matches a lower bound.\"}]",1784198865,35,{"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},"contextual-procurement-auctions-with-bandit-learning","",{"@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/contextual-procurement-auctions-with-bandit-learning/84859/",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 welfare goal in these contextual procurement auctions?","Question",{"text":75,"@type":76},"The mechanism targets welfare rather than revenue. Welfare regret is defined as the total surplus loss relative to the full-information efficient procurement rule.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"Why doesn’t the natural UCB allocation rule automatically ensure truthful bidding?",{"text":80,"@type":76},"Although the UCB rule achieves welfare regret under truthful bids, its adaptive bid-dependent learning path does not provide a truthfulness guarantee by itself.",{"name":82,"@type":73,"acceptedAnswer":83},"How do the proposed incentive mechanisms achieve truthfulness and low regret?",{"text":84,"@type":76},"The explore-then-commit mechanism uses bid-independent exploration and empirical critical payments to be dominant-strategy truthful. The frozen-payment UCB further freezes estimated payments after an initial exploration, enabling a tuned regret–incentive tradeoff that matches a lower bound.","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"]