{"id":"https://openalex.org/W4416776667","doi":"https://doi.org/10.48550/arxiv.2511.19656","title":"Lower Complexity Bounds for Nonconvex-Strongly-Convex Bilevel Optimization with First-Order Oracles","display_name":"Lower Complexity Bounds for Nonconvex-Strongly-Convex Bilevel Optimization with First-Order Oracles","publication_year":2025,"publication_date":"2025-11-24","ids":{"openalex":"https://openalex.org/W4416776667","doi":"https://doi.org/10.48550/arxiv.2511.19656"},"language":null,"primary_location":{"id":"pmh:oai:arXiv.org:2511.19656","is_oa":true,"landing_page_url":"https://arxiv.org/abs/2511.19656","pdf_url":"https://arxiv.org/pdf/2511.19656","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":"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/2511.19656","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5071973105","display_name":"Kaiyi Ji","orcid":"https://orcid.org/0000-0002-9533-0058"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Ji, Kaiyi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5071973105"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"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":0.6581000089645386,"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":0.6581000089645386,"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/T10545","display_name":"Optimization and Variational Analysis","score":0.24220000207424164,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.01850000023841858,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/bilevel-optimization","display_name":"Bilevel optimization","score":0.8300999999046326},{"id":"https://openalex.org/keywords/oracle","display_name":"Oracle","score":0.7712000012397766},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.6565999984741211},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.6141999959945679},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.4251999855041504},{"id":"https://openalex.org/keywords/focus","display_name":"Focus (optics)","score":0.39489999413490295},{"id":"https://openalex.org/keywords/stochastic-optimization","display_name":"Stochastic optimization","score":0.36410000920295715}],"concepts":[{"id":"https://openalex.org/C3309286","wikidata":"https://www.wikidata.org/wiki/Q4907693","display_name":"Bilevel optimization","level":3,"score":0.8300999999046326},{"id":"https://openalex.org/C55166926","wikidata":"https://www.wikidata.org/wiki/Q2892946","display_name":"Oracle","level":2,"score":0.7712000012397766},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6797999739646912},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.6565999984741211},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.6141999959945679},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5426999926567078},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.4251999855041504},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.40209999680519104},{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.39489999413490295},{"id":"https://openalex.org/C194387892","wikidata":"https://www.wikidata.org/wiki/Q1747770","display_name":"Stochastic optimization","level":2,"score":0.36410000920295715},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.34360000491142273},{"id":"https://openalex.org/C81845259","wikidata":"https://www.wikidata.org/wiki/Q290117","display_name":"Quadratic programming","level":2,"score":0.3149000108242035},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.3093000054359436},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.2802000045776367},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.2775000035762787},{"id":"https://openalex.org/C148043351","wikidata":"https://www.wikidata.org/wiki/Q4456944","display_name":"Current (fluid)","level":2,"score":0.2734000086784363},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.27090001106262207},{"id":"https://openalex.org/C94284585","wikidata":"https://www.wikidata.org/wiki/Q228184","display_name":"Random oracle","level":4,"score":0.26669999957084656},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.263700008392334}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2511.19656","is_oa":true,"landing_page_url":"https://arxiv.org/abs/2511.19656","pdf_url":"https://arxiv.org/pdf/2511.19656","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2511.19656","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2511.19656","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":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2511.19656","is_oa":true,"landing_page_url":"https://arxiv.org/abs/2511.19656","pdf_url":"https://arxiv.org/pdf/2511.19656","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5862580547","display_name":"Collaborative Research: CIF: Small: New Theory, Algorithms and Applications for Large-Scale Bilevel Optimization","funder_award_id":"2311274","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8414353436","display_name":"Collaborative Research: Distributed Bilevel Optimization in Multi-Agent Systems","funder_award_id":"2326592","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320337392","display_name":"Division of Electrical, Communications and Cyber Systems","ror":"https://ror.org/01krpsy48"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4416776667.pdf","grobid_xml":"https://content.openalex.org/works/W4416776667.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Although":[0],"upper":[1,122],"bound":[2],"guarantees":[3],"for":[4,82,87,126],"bilevel":[5,24,127,151],"optimization":[6,85,128,152],"have":[7],"been":[8,16],"widely":[9],"studied,":[10],"progress":[11],"on":[12,31],"lower":[13,44,79,124],"bounds":[14,45,80,111,125],"has":[15],"limited":[17],"due":[18],"to":[19,70],"the":[20,23,32,54,77,92,108,147],"complexity":[21,149],"of":[22,150],"structure.":[25],"In":[26,53,91],"this":[27],"work,":[28],"we":[29,57,95],"focus":[30],"smooth":[33],"nonconvex-strongly-convex":[34,88],"setting":[35],"and":[36,48,86,123,129],"develop":[37],"new":[38],"hard":[39],"instances":[40],"that":[41,59,97,131],"yield":[42],"nontrivial":[43],"under":[46,153],"deterministic":[47,55],"stochastic":[49,93,101],"first-order":[50,61,155],"oracle":[51,68,102],"models.":[52],"case,":[56,94],"prove":[58],"any":[60],"zero-respecting":[62],"algorithm":[63],"requires":[64],"at":[65,98],"least":[66,99],"$\u03a9(\u03ba^{3/2}\u03b5^{-2})$":[67],"calls":[69,103],"find":[71],"an":[72],"$\u03b5$-accurate":[73],"stationary":[74],"point,":[75],"improving":[76],"optimal":[78,148],"known":[81,110],"single-level":[83],"nonconvex":[84],"min-max":[89],"problems.":[90],"show":[96],"$\u03a9(\u03ba^{5/2}\u03b5^{-4})$":[100],"are":[104],"necessary,":[105],"again":[106],"strengthening":[107],"best":[109],"in":[112],"related":[113],"settings.":[114],"Our":[115],"results":[116],"expose":[117],"substantial":[118],"gaps":[119],"between":[120],"current":[121],"suggest":[130],"even":[132],"simplified":[133],"regimes,":[134],"such":[135],"as":[136],"those":[137],"with":[138],"quadratic":[139],"lower-level":[140],"objectives,":[141],"warrant":[142],"further":[143],"investigation":[144],"toward":[145],"understanding":[146],"standard":[154],"oracles.":[156]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2025-11-28T00:00:00"}