[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-85299-en":3,"doc-seo-85299-105":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},85299,687197207919,"Theodora","https://ap-avatar.wpscdn.com/avatar/a000253d6f5f7c60be?x-image-process=image/resize,m_fixed,w_180,h_180&k=1779446848396160552",8,"Research & Report","Decoupling Corruption and Horizon in Robust Contextual Pricing","Study robust repeated contextual pricing with linearly feature-dependent valuations. At each round, a seller observes a (possibly adversarial) context, posts a price, and receives corrupted binary sale feedback, with at most C rounds affected. The work designs an algorithm achieving regret O(Cd + d2 log T), where d is context dimension. This provides the first additive separation between corruption budget C and time horizon T for robust contextual pricing, resolving an open problem and extending robustness techniques to the pricing setting.","Decoupling Corruption and Horizon in Robust Contextual Pricing  \nMatteo Castiglioni∗  \nPolitecnico di Milano [matteo. castiglioni@polimi. it](matteo. castiglioni@polimi. it)  \nFrancesco Emanuele Stradi∗  \nPolitecnico di Milano [francescoemanuele. stradi@polimi. it](francescoemanuele. stradi@polimi. it)  \nAbstract  \narXiv :2607 . 1 12 10v 1 [ cs .GT] 13 Jul 2026  \nWe study robust repeated contextual pricing, where valuations depends linearly on the features. At each round t ∈ [T], a seller observes a context, posts a price, and receives only a possibly corrupted binary sale feedback. The seller knows an upper bound C on the number of corrupted rounds. We design an algorithm with regret O (Cd + d2 log T), where d is the context dimension. This is the first guarantee for robust contextual pricing that separates the dependence on the corruption budget C from the horizon T , closing the problem left open by Gupta, Guruganesh, Paes Leme, and Schneider (2025) .  \n∗ The authors are listed in alphabetical order.  \nContents  \n1 Introduction 3  \n1.1 Our Result and Techniques ................................ 3  \n1.2 Related Works and Why Existing Techniques Fail .................... 6  \n2 Contextual Pricing 7  \n2.1 Uncorrupted Contextual Pricing ............................. 7  \n2.2 Robust Contextual Pricing ................................ 8  \n3 Contextual Pricing with Proximity Feedback 8  \n3.1 Algorithmic Approach ................................... 8  \n3.2 A O (Cd + dlog T) Regret Bound ............................. 11  \n3.2.1 Committing Incurs Small Regret ......................... 11  \n3.2.2 Bounding Exploration Rounds with Far Medians ................ 13  \n3.2.3 Bounding Exploration Rounds with Close Medians ............... 13  \n3.2.4 Final Result ..................................... 16  \n4 From Proximity Feedback to Sale Feedback 16  \n4.1 Algorithmic Approach ................................... 17  \n4.2 A O (Cd + d2 log T) Regret Bound ............................ 17  \n5 Open Problems 19  \n1 Introduction  \nIn dynamic pricing [KL03], a seller repeatedly interacts with arriving buyers, posts prices, and observes only whether a sale occurred.  \nWe study the contextual variant of this problem, where valuations depend linearly on observable features. Formally, there is an unknown parameter θ⋆ , and at each round t, a context ut is revealed (chosen potentially adversarially) . The context deterministically determines the buyer’s valuation vt = ⟨θ⋆ , ut⟩ . After the seller posts a price pt, the only feedback is a binary sale indicator. The regret is measured against the clairvoyant benchmark that knows θ⋆ and posts vt in every round:  \nT  \nRT = X (vt − ptI{pt ≤ vt}) .  \nt=1  \nThis model captures feature-based pricing and is closely related to contextual search, where a learner must locate an unknown linear threshold from one-bit comparisons [CLL20, LLV18 , LS22 , LLS21] . Both problems are now well understood in the noise-free setting: geometric algorithms based on maintaining and cutting a feasible parameter set achieve nearly optimal regret [LLV18, LS22 , LLS21], with the optimal horizon dependence for contextual pricing settled at Θ(d log log T) [LLS21] .  \nThese algorithms are, however, fundamentally fragile. They rely on the assumption that every sale bit faithfully reflects the buyer’s true valuation. A natural robustness question is: what happens when an adversary can corrupt the feedback in up to C rounds, modeling, for example, buyers who act irrationally or strategically?  \nPrior work on robust contextual pricing [KLPS21, GGLS25] has made significant progress, but all existing bounds couple the corruption term and the horizon multiplicatively. The current state of the art, due to [GGLS25], achieves O (Cd log log T), and their lower bound rules out a fully additive O (C + d log log T) guarantee. This leaves open the following question:  \nCan we design robust contextual pricing algorithms with regret O((C + log T) · poly(d))?  \n","cbCairqSbU9MUQs3","https://ap.wps.com/l/cbCairqSbU9MUQs3","pdf",382292,2,1,20,"English","en",105,"# Introduction\n## Our Result and Techniques\n# Contextual Pricing\n## Uncorrupted Contextual Pricing\n## Robust Contextual Pricing\n# Contextual Pricing with Proximity Feedback\n## Algorithmic Approach\n## A O(Cd + dlog T) Regret Bound\n# From Proximity Feedback to Sale Feedback\n## Algorithmic Approach\n## A O(Cd + d2 log T) Regret Bound\n# Open Problems","[{\"question\":\"What problem does the document address?\",\"answer\":\"It studies robust repeated contextual pricing where valuations depend linearly on observed features and the seller sees only corrupted binary sale feedback.\"},{\"question\":\"How is robustness modeled in the paper?\",\"answer\":\"An adversary corrupts the sale feedback in up to C rounds, capturing irrational or strategic buyer behavior while the seller knows an upper bound C.\"},{\"question\":\"What regret guarantee is proved?\",\"answer\":\"The paper provides an algorithm with regret O(Cd + d2 log T), achieving an additive separation between the corruption budget C and the horizon T.\"}]",1784202326,50,{"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},"decoupling-corruption-and-horizon-in-robust-contextual-pricing","",{"@graph":36,"@context":85},[37,53,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,47,50],{"item":41,"name":42,"@type":43,"position":21},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":20},"https://docshare.wps.com/document/","Document",{"item":48,"name":12,"@type":43,"position":49},"https://docshare.wps.com/document/research-report/",3,{"item":51,"name":13,"@type":43,"position":52},"https://docshare.wps.com/document/decoupling-corruption-and-horizon-in-robust-contextual-pricing/85299/",4,{"url":51,"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},"What problem does the document address?","Question",{"text":75,"@type":76},"It studies robust repeated contextual pricing where valuations depend linearly on observed features and the seller sees only corrupted binary sale feedback.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How is robustness modeled in the paper?",{"text":80,"@type":76},"An adversary corrupts the sale feedback in up to C rounds, capturing irrational or strategic buyer behavior while the seller knows an upper bound C.",{"name":82,"@type":73,"acceptedAnswer":83},"What regret guarantee is proved?",{"text":84,"@type":76},"The paper provides an algorithm with regret O(Cd + d2 log T), achieving an additive separation between the corruption budget C and the horizon T.","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":25},{"code":4,"msg":5,"data":92},[93,97,101,105,110,114,119,122,126,129,133],{"id":21,"doc_module":4,"doc_module_name":46,"category_name":94,"show_sort_weight":95,"slug":96},"Story & Novel",90,"story-novel",{"id":20,"doc_module":4,"doc_module_name":46,"category_name":98,"show_sort_weight":99,"slug":100},"Literature",80,"literature",{"id":52,"doc_module":4,"doc_module_name":46,"category_name":102,"show_sort_weight":103,"slug":104},"Exam",70,"exam",{"id":106,"doc_module":4,"doc_module_name":46,"category_name":107,"show_sort_weight":108,"slug":109},5,"Comic",60,"comic",{"id":111,"doc_module":4,"doc_module_name":46,"category_name":112,"show_sort_weight":29,"slug":113},6,"Technology","technology",{"id":115,"doc_module":4,"doc_module_name":46,"category_name":116,"show_sort_weight":117,"slug":118},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":120,"slug":121},30,"research-report",{"id":123,"doc_module":4,"doc_module_name":46,"category_name":124,"show_sort_weight":22,"slug":125},9,"Religion & Spirituality","religion-spirituality",{"id":22,"doc_module":4,"doc_module_name":46,"category_name":127,"show_sort_weight":22,"slug":128},"World Cup","world-cup",{"id":130,"doc_module":4,"doc_module_name":46,"category_name":131,"show_sort_weight":130,"slug":132},10,"Lifestyle","lifestyle",{"id":134,"doc_module":4,"doc_module_name":46,"category_name":135,"show_sort_weight":106,"slug":136},19,"General","general"]