{"id":"https://openalex.org/W7160846639","doi":"https://doi.org/10.48550/arxiv.2605.07239","title":"Sample Complexity of Stochastic Optimization with Integer Variables","display_name":"Sample Complexity of Stochastic Optimization with Integer Variables","publication_year":2026,"publication_date":"2026-05-08","ids":{"openalex":"https://openalex.org/W7160846639","doi":"https://doi.org/10.48550/arxiv.2605.07239"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2605.07239","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.07239","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,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2605.07239","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5124761061","display_name":"Hongyu Cheng","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Cheng, Hongyu","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5135849469","display_name":"Yinghao Zheng","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zheng, Yinghao","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5135852688","display_name":"Marco Molinaro","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Molinaro, Marco","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5048617506","display_name":"Amitabh Basu","orcid":"https://orcid.org/0000-0002-1070-2626"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Basu, Amitabh","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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.5582000017166138,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.5582000017166138,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T11413","display_name":"Risk and Portfolio Optimization","score":0.35499998927116394,"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/T12101","display_name":"Advanced Bandit Algorithms Research","score":0.019099999219179153,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/stochastic-optimization","display_name":"Stochastic optimization","score":0.7591999769210815},{"id":"https://openalex.org/keywords/continuous-optimization","display_name":"Continuous optimization","score":0.7224000096321106},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.6442000269889832},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.6341999769210815},{"id":"https://openalex.org/keywords/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.6000000238418579},{"id":"https://openalex.org/keywords/sample","display_name":"Sample (material)","score":0.41260001063346863},{"id":"https://openalex.org/keywords/computational-complexity-theory","display_name":"Computational complexity theory","score":0.39079999923706055},{"id":"https://openalex.org/keywords/stochastic-programming","display_name":"Stochastic programming","score":0.38420000672340393},{"id":"https://openalex.org/keywords/vector-optimization","display_name":"Vector optimization","score":0.3659000098705292}],"concepts":[{"id":"https://openalex.org/C194387892","wikidata":"https://www.wikidata.org/wiki/Q1747770","display_name":"Stochastic optimization","level":2,"score":0.7591999769210815},{"id":"https://openalex.org/C92995354","wikidata":"https://www.wikidata.org/wiki/Q5165499","display_name":"Continuous optimization","level":4,"score":0.7224000096321106},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7077000141143799},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.6442000269889832},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.6341999769210815},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.6000000238418579},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5713000297546387},{"id":"https://openalex.org/C198531522","wikidata":"https://www.wikidata.org/wiki/Q485146","display_name":"Sample (material)","level":2,"score":0.41260001063346863},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.39079999923706055},{"id":"https://openalex.org/C137631369","wikidata":"https://www.wikidata.org/wiki/Q7617831","display_name":"Stochastic programming","level":2,"score":0.38420000672340393},{"id":"https://openalex.org/C164088818","wikidata":"https://www.wikidata.org/wiki/Q7917833","display_name":"Vector optimization","level":4,"score":0.3659000098705292},{"id":"https://openalex.org/C129848803","wikidata":"https://www.wikidata.org/wiki/Q2564360","display_name":"Sample size determination","level":2,"score":0.3601999878883362},{"id":"https://openalex.org/C145671259","wikidata":"https://www.wikidata.org/wiki/Q1493786","display_name":"Discrete optimization","level":3,"score":0.35850000381469727},{"id":"https://openalex.org/C2778445095","wikidata":"https://www.wikidata.org/wiki/Q18354077","display_name":"Sample complexity","level":2,"score":0.34279999136924744},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.33239999413490295},{"id":"https://openalex.org/C193254401","wikidata":"https://www.wikidata.org/wiki/Q2160088","display_name":"Robust optimization","level":2,"score":0.3321000039577484},{"id":"https://openalex.org/C2983394010","wikidata":"https://www.wikidata.org/wiki/Q19885330","display_name":"Continuous variable","level":2,"score":0.3312000036239624},{"id":"https://openalex.org/C109578324","wikidata":"https://www.wikidata.org/wiki/Q3354463","display_name":"Random optimization","level":5,"score":0.32899999618530273},{"id":"https://openalex.org/C164752517","wikidata":"https://www.wikidata.org/wiki/Q5570875","display_name":"Global optimization","level":2,"score":0.31540000438690186},{"id":"https://openalex.org/C62114133","wikidata":"https://www.wikidata.org/wiki/Q5366944","display_name":"L-reduction","level":5,"score":0.3082999885082245},{"id":"https://openalex.org/C56086750","wikidata":"https://www.wikidata.org/wiki/Q6042592","display_name":"Integer programming","level":2,"score":0.3068000078201294},{"id":"https://openalex.org/C55660270","wikidata":"https://www.wikidata.org/wiki/Q5164377","display_name":"Constrained optimization","level":2,"score":0.3043000102043152},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.30070000886917114},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.29600000381469727}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2605.07239","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.07239","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,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2605.07239","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.07239","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,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0,27],"establish":[1,123],"sample":[2,105,125,183],"complexity":[3,18,66,126,157,184],"results":[4,127],"for":[5,128],"stochastic":[6,69,79,131],"optimization":[7,25,31,73,81,100,132,153,169,188],"over":[8,58,90],"the":[9,17,22,47,50,61,64,76,93,109,135,160,180,186],"integers,":[10],"especially":[11],"with":[12,19,82],"a":[13,113],"view":[14],"to":[15,21,108,118,134,159,173,179],"understand":[16],"respect":[20],"corresponding":[23],"continuous":[24,110,130,161,187],"problem.":[26],"show":[28,97,166],"that":[29,98,167],"integer":[30,99,152,168],"can":[32,101],"sometimes":[33,39],"require":[34,102],"strictly":[35,40,103],"more":[36],"samples":[37,172],"and":[38,52],"smaller":[41],"number":[42],"of":[43,49,60,67,92,137],"samples,":[44],"depending":[45],"on":[46],"structure":[48],"objective":[51],"constraints.":[53,85],"1.":[54],"For":[55,87,147],"Lipschitz":[56,88],"objectives":[57,89],"subsets":[59,91],"$\\ell_\\infty$":[62],"ball,":[63,95],"statistical":[65,156],"general":[68],"mixed-integer,":[70],"nonlinear,":[71],"nonconvex":[72,129],"is":[74],"exactly":[75],"same":[77],"as":[78],"linear":[80],"just":[83],"bound":[84],"2.":[86],"$\\ell_2$":[94],"we":[96,121,165],"*smaller*":[104],"size":[106],"compared":[107,158,178],"setting":[111],"in":[112,143],"certain":[114],"regime.":[115],"To":[116],"get":[117],"this":[119],"result,":[120],"also":[122],"tight":[124],"which,":[133],"best":[136],"our":[138],"knowledge,":[139],"do":[140],"not":[141],"appear":[142],"prior":[144],"work.":[145],"3.":[146],"strongly":[148],"convex,":[149],"smooth":[150],"objectives,":[151],"has":[154],"high":[155],"setting.":[162],"In":[163],"particular,":[164],"requires":[170],"$\u03a9(1/\u03b5^2)$":[171],"report":[174],"an":[175],"$\u03b5$-approximate":[176],"solution,":[177],"well-known":[181],"$O(1/\u03b5)$":[182],"from":[185],"literature.":[189]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-05-12T00:00:00"}
