{"id":"https://openalex.org/W4415125260","doi":"https://doi.org/10.48550/arxiv.2506.12994","title":"Differentially Private Bilevel Optimization: Efficient Algorithms with Near-Optimal Rates","display_name":"Differentially Private Bilevel Optimization: Efficient Algorithms with Near-Optimal Rates","publication_year":2025,"publication_date":"2025-06-15","ids":{"openalex":"https://openalex.org/W4415125260","doi":"https://doi.org/10.48550/arxiv.2506.12994"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2506.12994","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2506.12994","pdf_url":"https://arxiv.org/pdf/2506.12994","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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"},"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2506.12994","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5089839809","display_name":"Andrew M. Lowy","orcid":"https://orcid.org/0000-0002-7106-0735"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Lowy, Andrew","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5030021626","display_name":"Daogao Liu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Liu, Daogao","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5089839809"],"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/T10067","display_name":"Stochastic processes and financial applications","score":0.9972000122070312,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9972000122070312,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11413","display_name":"Risk and Portfolio Optimization","score":0.9729999899864197,"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/T11545","display_name":"Advanced Banach Space Theory","score":0.9538000226020813,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/bilevel-optimization","display_name":"Bilevel optimization","score":0.698199987411499},{"id":"https://openalex.org/keywords/hyperparameter","display_name":"Hyperparameter","score":0.6133000254631042},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.5371000170707703},{"id":"https://openalex.org/keywords/population","display_name":"Population","score":0.47380000352859497},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.45910000801086426},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4318000078201294},{"id":"https://openalex.org/keywords/implementation","display_name":"Implementation","score":0.4172999858856201},{"id":"https://openalex.org/keywords/key","display_name":"Key (lock)","score":0.4016000032424927}],"concepts":[{"id":"https://openalex.org/C3309286","wikidata":"https://www.wikidata.org/wiki/Q4907693","display_name":"Bilevel optimization","level":3,"score":0.698199987411499},{"id":"https://openalex.org/C8642999","wikidata":"https://www.wikidata.org/wiki/Q4171168","display_name":"Hyperparameter","level":2,"score":0.6133000254631042},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5849000215530396},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.5371000170707703},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.49059998989105225},{"id":"https://openalex.org/C2908647359","wikidata":"https://www.wikidata.org/wiki/Q2625603","display_name":"Population","level":2,"score":0.47380000352859497},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4702000021934509},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.45910000801086426},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4318000078201294},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4296000003814697},{"id":"https://openalex.org/C26713055","wikidata":"https://www.wikidata.org/wiki/Q245962","display_name":"Implementation","level":2,"score":0.4172999858856201},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.4016000032424927},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.3801000118255615},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.349700003862381},{"id":"https://openalex.org/C23130292","wikidata":"https://www.wikidata.org/wiki/Q5275358","display_name":"Differential privacy","level":2,"score":0.3407000005245209},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.33149999380111694},{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.3273000121116638},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.32339999079704285},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.2858999967575073},{"id":"https://openalex.org/C173801870","wikidata":"https://www.wikidata.org/wiki/Q201413","display_name":"Heuristic","level":2,"score":0.2766000032424927},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.2653999924659729},{"id":"https://openalex.org/C140779682","wikidata":"https://www.wikidata.org/wiki/Q210868","display_name":"Sampling (signal processing)","level":3,"score":0.2596000134944916},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.2581000030040741},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.2531000077724457}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2506.12994","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2506.12994","pdf_url":"https://arxiv.org/pdf/2506.12994","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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.2506.12994","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2506.12994","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2506.12994","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2506.12994","pdf_url":"https://arxiv.org/pdf/2506.12994","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Bilevel":[0],"optimization,":[1],"in":[2,124],"which":[3,154],"one":[4],"optimization":[5],"problem":[6],"is":[7,58,141],"nested":[8,107],"inside":[9],"another,":[10],"underlies":[11],"many":[12],"machine":[13],"learning":[14],"applications":[15,28],"with":[16,168],"a":[17,142],"hierarchical":[18],"structure":[19],"--":[20],"such":[21],"as":[22],"meta-learning":[23],"and":[24,60,64,75,84,133,145],"hyperparameter":[25],"optimization.":[26,48,119],"Such":[27],"often":[29],"involve":[30],"sensitive":[31],"training":[32],"data,":[33],"raising":[34],"pressing":[35],"concerns":[36],"about":[37],"individual":[38],"privacy.":[39,78],"Motivated":[40],"by":[41],"this,":[42],"we":[43,164],"study":[44],"differentially":[45,93],"private":[46,94],"bilevel":[47,108,117],"We":[49,110],"first":[50],"focus":[51],"on":[52,67,183],"settings":[53],"where":[54],"the":[55,68,87,102,106,131,161,184,187],"outer-level":[56],"objective":[57],"convex,":[59],"provide":[61,112],"novel":[62,166],"upper":[63],"lower":[65],"bounds":[66,80,115,121,179],"excess":[69],"empirical":[70],"risk":[71],"for":[72,90,116,171],"both":[73],"pure":[74],"approximate":[76,174],"differential":[77],"These":[79],"are":[81,122],"nearly":[82],"tight":[83],"essentially":[85],"match":[86],"optimal":[88],"rates":[89,170],"standard":[91],"single-level":[92],"ERM,":[95],"up":[96],"to":[97],"additional":[98],"terms":[99],"that":[100],"capture":[101],"intrinsic":[103],"complexity":[104],"of":[105,130,147,157,186],"structure.":[109],"also":[111],"population":[113],"loss":[114],"stochastic":[118],"The":[120],"achieved":[123],"polynomial":[125],"time":[126],"via":[127],"efficient":[128],"implementations":[129],"exponential":[132,135],"regularized":[134],"mechanisms.":[136],"A":[137],"key":[138],"technical":[139],"contribution":[140],"new":[143],"method":[144],"analysis":[146],"log-concave":[148],"sampling":[149],"under":[150],"inexact":[151],"function":[152],"evaluations,":[153],"may":[155],"be":[156],"independent":[158],"interest.":[159],"In":[160],"non-convex":[162],"setting,":[163],"develop":[165],"algorithms":[167],"state-of-the-art":[169],"privately":[172],"finding":[173],"stationary":[175],"points.":[176],"Notably,":[177],"our":[178],"do":[180],"not":[181],"depend":[182],"dimension":[185],"inner":[188],"problem.":[189]},"counts_by_year":[],"updated_date":"2026-03-07T16:01:11.037858","created_date":"2025-10-14T00:00:00"}
