{"id":"https://openalex.org/W7225148351","doi":"https://doi.org/10.48550/arxiv.2611.03199","title":"Cold-Start Pricing of LLM Services under Two-Sided Learning","display_name":"Cold-Start Pricing of LLM Services under Two-Sided Learning","publication_year":2026,"publication_date":"2026-11-02","ids":{"openalex":"https://openalex.org/W7225148351","doi":"https://doi.org/10.48550/arxiv.2611.03199"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2611.03199","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2611.03199","pdf_url":"https://arxiv.org/pdf/2611.03199","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2611.03199","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5137664511","display_name":"Zhicheng Du","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Du, Zhicheng","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5025408809","display_name":"Pinyan Lu","orcid":"https://orcid.org/0009-0005-0569-4122","observed_orcids":["https://orcid.org/0009-0005-0569-4122"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lu, Pinyan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5160457153","display_name":"Keyu Wang","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wang, Keyu","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5160487819","display_name":"Zihe Wang","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wang, Zihe","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5160541445","display_name":"Xiang Yan","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yan, Xiang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5010124542","display_name":"Yang Chunxue","orcid":"https://orcid.org/0000-0002-0209-7200","observed_orcids":["https://orcid.org/0000-0002-0209-7200"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yang, Chunxue","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12101","display_name":"Advanced Bandit Algorithms Research","score":0.9624000191688538,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T12101","display_name":"Advanced Bandit Algorithms Research","score":0.9624000191688538,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T12288","display_name":"Optimization and Search Problems","score":0.01640000008046627,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10328","display_name":"Supply Chain and Inventory Management","score":0.005400000140070915,"subfield":{"id":"https://openalex.org/subfields/1404","display_name":"Management Information Systems"},"field":{"id":"https://openalex.org/fields/14","display_name":"Business, Management and Accounting"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/large-language-models","display_name":"large language models","score":0.7940000295639038},{"id":"https://openalex.org/keywords/online-pricing","display_name":"online pricing","score":0.6579999923706055},{"id":"https://openalex.org/keywords/willingness-to-pay","display_name":"willingness to pay","score":0.7369999885559082},{"id":"https://openalex.org/keywords/phase-transitions","display_name":"phase transitions","score":0.5509999990463257},{"id":"https://openalex.org/keywords/dynamic-pricing","display_name":"dynamic pricing","score":0.5860000252723694}],"concepts":[{"id":"https://openalex.org/C50817715","wikidata":"https://www.wikidata.org/wiki/Q79895177","display_name":"Regret","level":2,"score":0.8639000058174133},{"id":"https://openalex.org/C116537","wikidata":"https://www.wikidata.org/wiki/Q2169973","display_name":"Service provider","level":3,"score":0.6327000260353088},{"id":"https://openalex.org/C181622380","wikidata":"https://www.wikidata.org/wiki/Q26911","display_name":"Profit (economics)","level":2,"score":0.5612999796867371},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5590000152587891},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.435699999332428},{"id":"https://openalex.org/C28761237","wikidata":"https://www.wikidata.org/wiki/Q7805321","display_name":"Time horizon","level":2,"score":0.42980000376701355},{"id":"https://openalex.org/C99221444","wikidata":"https://www.wikidata.org/wiki/Q1532069","display_name":"Private information retrieval","level":2,"score":0.4092000126838684},{"id":"https://openalex.org/C2777338717","wikidata":"https://www.wikidata.org/wiki/Q1762621","display_name":"Vendor","level":2,"score":0.38940000534057617},{"id":"https://openalex.org/C2777364431","wikidata":"https://www.wikidata.org/wiki/Q140813","display_name":"Willingness to pay","level":2,"score":0.3555999994277954},{"id":"https://openalex.org/C189560676","wikidata":"https://www.wikidata.org/wiki/Q1187906","display_name":"Profit margin","level":2,"score":0.35019999742507935},{"id":"https://openalex.org/C42475967","wikidata":"https://www.wikidata.org/wiki/Q194292","display_name":"Operations research","level":1,"score":0.3427000045776367},{"id":"https://openalex.org/C2780378061","wikidata":"https://www.wikidata.org/wiki/Q25351891","display_name":"Service (business)","level":2,"score":0.32690000534057617},{"id":"https://openalex.org/C175444787","wikidata":"https://www.wikidata.org/wiki/Q39072","display_name":"Microeconomics","level":1,"score":0.3149999976158142},{"id":"https://openalex.org/C162118730","wikidata":"https://www.wikidata.org/wiki/Q1128453","display_name":"Actuarial science","level":1,"score":0.3109000027179718},{"id":"https://openalex.org/C68359772","wikidata":"https://www.wikidata.org/wiki/Q185715","display_name":"Opportunity cost","level":2,"score":0.301800012588501},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.29820001125335693},{"id":"https://openalex.org/C2986087404","wikidata":"https://www.wikidata.org/wiki/Q15946010","display_name":"Online learning","level":2,"score":0.29820001125335693},{"id":"https://openalex.org/C149728462","wikidata":"https://www.wikidata.org/wiki/Q751319","display_name":"Minimax","level":2,"score":0.2978000044822693},{"id":"https://openalex.org/C21782646","wikidata":"https://www.wikidata.org/wiki/Q841666","display_name":"Search cost","level":2,"score":0.29499998688697815},{"id":"https://openalex.org/C12725497","wikidata":"https://www.wikidata.org/wiki/Q810247","display_name":"Baseline (sea)","level":2,"score":0.2872999906539917},{"id":"https://openalex.org/C144133560","wikidata":"https://www.wikidata.org/wiki/Q4830453","display_name":"Business","level":0,"score":0.2822999954223633},{"id":"https://openalex.org/C774472","wikidata":"https://www.wikidata.org/wiki/Q6760393","display_name":"Margin (machine learning)","level":2,"score":0.2768999934196472},{"id":"https://openalex.org/C196921405","wikidata":"https://www.wikidata.org/wiki/Q786431","display_name":"Online algorithm","level":2,"score":0.27000001072883606},{"id":"https://openalex.org/C46934059","wikidata":"https://www.wikidata.org/wiki/Q61515","display_name":"Outsourcing","level":2,"score":0.2630999982357025}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2611.03199","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2611.03199","pdf_url":"https://arxiv.org/pdf/2611.03199","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2611.03199","doi":"https://doi.org/10.48550/arxiv.2611.03199","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2611.03199","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2611.03199","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2611.03199","pdf_url":"https://arxiv.org/pdf/2611.03199","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4416237307","https://openalex.org/W7204103169","https://openalex.org/W7164665059","https://openalex.org/W4411945969","https://openalex.org/W7165396607","https://openalex.org/W4399994184","https://openalex.org/W7206149273","https://openalex.org/W4407425907","https://openalex.org/W7154936181","https://openalex.org/W4416063909"],"abstract_inverted_index":{"Online":[0],"large":[1],"language":[2],"model":[3],"(LLM)":[4],"services":[5],"face":[6],"a":[7,38,43,46,59],"pricing":[8],"cold":[9],"start:":[10],"providers":[11],"initially":[12],"lack":[13],"the":[14,56,91,105,126,131,135,149,167,178,193],"historical":[15],"data":[16],"and":[17,45,62,101,182],"user":[18,49],"information":[19],"needed":[20],"for":[21],"precise":[22],"pricing,":[23],"while":[24],"users'":[25],"willingness":[26,86],"to":[27,70,79,81,87,172],"pay":[28,88],"evolves":[29],"with":[30,145],"repeated":[31],"use.":[32],"We":[33,97],"formulate":[34],"this":[35],"challenge":[36,77],"as":[37],"\\emph{two-sided":[39],"learning}":[40],"problem":[41],"between":[42],"provider":[44,57,136],"user.":[47],"The":[48,74],"learns":[50],"from":[51],"private":[52,92],"usage":[53],"experience,":[54],"whereas":[55],"incurs":[58],"serving":[60,116,158],"cost":[61],"dynamically":[63],"adapts":[64],"prices":[65],"using":[66],"only":[67,162],"purchase":[68],"decisions":[69],"maximize":[71],"cumulative":[72],"profit.":[73],"provider's":[75],"central":[76],"is":[78,142],"learn":[80,138],"price":[82,173],"against":[83],"an":[84],"evolving":[85],"without":[89],"observing":[90],"experiences":[93],"driving":[94],"that":[95,157,184],"evolution.":[96],"establish":[98],"matching":[99],"upper":[100],"lower":[102],"bounds":[103],"on":[104],"minimax":[106],"regret":[107,180],"over":[108],"horizon":[109],"$T$,":[110],"identifying":[111],"two":[112],"cost-dependent":[113],"regimes.":[114],"When":[115],"costs":[117,159],"are":[118],"sufficiently":[119],"low,":[120],"our":[121,185],"Calibration-and-Tracking":[122,144],"(CAT)":[123],"algorithm":[124],"achieves":[125],"optimal":[127,150],"rate":[128,151],"$\u0398(T^{1/3})$.":[129],"In":[130],"higher-cost":[132],"regime,":[133],"where":[134],"must":[137],"whether":[139],"continued":[140],"service":[141],"profitable,":[143],"Retirement":[146],"(CAT-R)":[147],"attains":[148],"$\u0398(\\sqrt{T})$.":[152],"This":[153],"phase":[154],"transition":[155],"shows":[156],"affect":[160],"not":[161],"profit":[163],"margins":[164],"but":[165],"also":[166],"fundamental":[168],"difficulty":[169],"of":[170],"learning":[171,190],"LLM":[174],"services.":[175],"Simulations":[176],"support":[177],"predicted":[179],"scaling":[181],"show":[183],"algorithms":[186],"outperform":[187],"standard":[188],"online":[189],"baselines":[191],"in":[192],"evaluated":[194],"settings.":[195]},"counts_by_year":[],"updated_date":"2026-11-05T12:25:35.769452","created_date":"2026-11-04T00:00:00"}