{"id":"https://openalex.org/W4408564942","doi":"https://doi.org/10.1109/tpami.2025.3552197","title":"Revisiting Stochastic Multi-Level Compositional Optimization","display_name":"Revisiting Stochastic Multi-Level Compositional Optimization","publication_year":2025,"publication_date":"2025-03-18","ids":{"openalex":"https://openalex.org/W4408564942","doi":"https://doi.org/10.1109/tpami.2025.3552197","pmid":"https://pubmed.ncbi.nlm.nih.gov/40100654"},"language":"en","primary_location":{"id":"doi:10.1109/tpami.2025.3552197","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tpami.2025.3552197","pdf_url":null,"source":{"id":"https://openalex.org/S199944782","display_name":"IEEE Transactions on Pattern Analysis and Machine Intelligence","issn_l":"0162-8828","issn":["0162-8828","1939-3539","2160-9292"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320439","host_organization_name":"IEEE Computer Society","host_organization_lineage":["https://openalex.org/P4310320439","https://openalex.org/P4310319808"],"host_organization_lineage_names":["IEEE Computer Society","Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Pattern Analysis and Machine Intelligence","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Wei Jiang","orcid":"https://orcid.org/0009-0007-4595-1060"},"institutions":[{"id":"https://openalex.org/I881766915","display_name":"Nanjing University","ror":"https://ror.org/01rxvg760","country_code":"CN","type":"education","lineage":["https://openalex.org/I881766915"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Wei Jiang","raw_affiliation_strings":["National Key Laboratory for Novel Software Technology, Nanjing University, Nanjing, China"],"raw_orcid":"https://orcid.org/0009-0007-4595-1060","affiliations":[{"raw_affiliation_string":"National Key Laboratory for Novel Software Technology, Nanjing University, Nanjing, China","institution_ids":["https://openalex.org/I881766915"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Sifan Yang","orcid":"https://orcid.org/0009-0000-1201-8476"},"institutions":[{"id":"https://openalex.org/I4210101451","display_name":"Nanjing University of Industry Technology","ror":"https://ror.org/00qf07q44","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210101451"]},{"id":"https://openalex.org/I881766915","display_name":"Nanjing University","ror":"https://ror.org/01rxvg760","country_code":"CN","type":"education","lineage":["https://openalex.org/I881766915"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Sifan Yang","raw_affiliation_strings":["National Key Laboratory for Novel Software Technology, School of Artiicial Intelligence, Nanjing University, Nanjing, China","National Key Laboratory for Novel Software Technology, and School of Artiicial Intelligence, Nanjing University, Nanjing, China"],"raw_orcid":"https://orcid.org/0009-0000-1201-8476","affiliations":[{"raw_affiliation_string":"National Key Laboratory for Novel Software Technology, School of Artiicial Intelligence, Nanjing University, Nanjing, China","institution_ids":["https://openalex.org/I4210101451"]},{"raw_affiliation_string":"National Key Laboratory for Novel Software Technology, and School of Artiicial Intelligence, Nanjing University, Nanjing, China","institution_ids":["https://openalex.org/I881766915"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Yibo Wang","orcid":"https://orcid.org/0009-0006-7410-6854"},"institutions":[{"id":"https://openalex.org/I4210101451","display_name":"Nanjing University of Industry Technology","ror":"https://ror.org/00qf07q44","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210101451"]},{"id":"https://openalex.org/I881766915","display_name":"Nanjing University","ror":"https://ror.org/01rxvg760","country_code":"CN","type":"education","lineage":["https://openalex.org/I881766915"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yibo Wang","raw_affiliation_strings":["National Key Laboratory for Novel Software Technology, School of Artiicial Intelligence, Nanjing University, Nanjing, China","National Key Laboratory for Novel Software Technology, and School of Artiicial Intelligence, Nanjing University, Nanjing, China"],"raw_orcid":"https://orcid.org/0009-0006-7410-6854","affiliations":[{"raw_affiliation_string":"National Key Laboratory for Novel Software Technology, School of Artiicial Intelligence, Nanjing University, Nanjing, China","institution_ids":["https://openalex.org/I4210101451"]},{"raw_affiliation_string":"National Key Laboratory for Novel Software Technology, and School of Artiicial Intelligence, Nanjing University, Nanjing, China","institution_ids":["https://openalex.org/I881766915"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5023288846","display_name":"Tianbao Yang","orcid":"https://orcid.org/0000-0002-7858-5438"},"institutions":[{"id":"https://openalex.org/I91045830","display_name":"Texas A&M University","ror":"https://ror.org/01f5ytq51","country_code":"US","type":"education","lineage":["https://openalex.org/I91045830"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Tianbao Yang","raw_affiliation_strings":["Department of Computer Science and Engineering, Texas A&M University, College Station, TX, USA","Department of Computer Science and Engineering, Texas A&M University, College Station, TX, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Engineering, Texas A&M University, College Station, TX, USA","institution_ids":["https://openalex.org/I91045830"]},{"raw_affiliation_string":"Department of Computer Science and Engineering, Texas A&M University, College Station, TX, USA","institution_ids":["https://openalex.org/I91045830"]}]},{"author_position":"last","author":{"id":null,"display_name":"Lijun Zhang","orcid":"https://orcid.org/0000-0002-5138-3182"},"institutions":[{"id":"https://openalex.org/I4210101451","display_name":"Nanjing University of Industry Technology","ror":"https://ror.org/00qf07q44","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210101451"]},{"id":"https://openalex.org/I881766915","display_name":"Nanjing University","ror":"https://ror.org/01rxvg760","country_code":"CN","type":"education","lineage":["https://openalex.org/I881766915"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Lijun Zhang","raw_affiliation_strings":["National Key Laboratory for Novel Software Technology, School of Artiicial Intelligence, Nanjing University, Nanjing, China","National Key Laboratory for Novel Software Technology, and School of Artiicial Intelligence, Nanjing University, Nanjing, China"],"raw_orcid":"https://orcid.org/0000-0002-5138-3182","affiliations":[{"raw_affiliation_string":"National Key Laboratory for Novel Software Technology, School of Artiicial Intelligence, Nanjing University, Nanjing, China","institution_ids":["https://openalex.org/I4210101451"]},{"raw_affiliation_string":"National Key Laboratory for Novel Software Technology, and School of Artiicial Intelligence, Nanjing University, Nanjing, China","institution_ids":["https://openalex.org/I881766915"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I881766915"],"apc_list":null,"apc_paid":null,"fwci":1.025,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.72582876,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"47","issue":"7","first_page":"5613","last_page":"5624"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11801","display_name":"Reservoir Engineering and Simulation Methods","score":0.9563999772071838,"subfield":{"id":"https://openalex.org/subfields/2212","display_name":"Ocean Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11801","display_name":"Reservoir Engineering and Simulation Methods","score":0.9563999772071838,"subfield":{"id":"https://openalex.org/subfields/2212","display_name":"Ocean Engineering"},"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/computer-science","display_name":"Computer science","score":0.6109878420829773},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.537859320640564}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6109878420829773},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.537859320640564}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tpami.2025.3552197","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tpami.2025.3552197","pdf_url":null,"source":{"id":"https://openalex.org/S199944782","display_name":"IEEE Transactions on Pattern Analysis and Machine Intelligence","issn_l":"0162-8828","issn":["0162-8828","1939-3539","2160-9292"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320439","host_organization_name":"IEEE Computer Society","host_organization_lineage":["https://openalex.org/P4310320439","https://openalex.org/P4310319808"],"host_organization_lineage_names":["IEEE Computer Society","Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Pattern Analysis and Machine Intelligence","raw_type":"journal-article"},{"id":"pmid:40100654","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/40100654","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE transactions on pattern analysis and machine intelligence","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G7911040224","display_name":null,"funder_award_id":"U23A20382","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":48,"referenced_works":["https://openalex.org/W1494085563","https://openalex.org/W1818156433","https://openalex.org/W1950214537","https://openalex.org/W2096840748","https://openalex.org/W2100371547","https://openalex.org/W2612083123","https://openalex.org/W2767614206","https://openalex.org/W2963313444","https://openalex.org/W2989715069","https://openalex.org/W2993258424","https://openalex.org/W3011766119","https://openalex.org/W3080245286","https://openalex.org/W3081147848","https://openalex.org/W3140913729","https://openalex.org/W3154049590","https://openalex.org/W4252698487","https://openalex.org/W4395028151","https://openalex.org/W4400378610","https://openalex.org/W6631190155","https://openalex.org/W6674709963","https://openalex.org/W6675761068","https://openalex.org/W6676105031","https://openalex.org/W6677984395","https://openalex.org/W6681435938","https://openalex.org/W6713057566","https://openalex.org/W6726059432","https://openalex.org/W6728561528","https://openalex.org/W6734509502","https://openalex.org/W6736057607","https://openalex.org/W6745375793","https://openalex.org/W6747620207","https://openalex.org/W6753122105","https://openalex.org/W6755743750","https://openalex.org/W6757751764","https://openalex.org/W6763249885","https://openalex.org/W6763288952","https://openalex.org/W6765176130","https://openalex.org/W6767091436","https://openalex.org/W6772150479","https://openalex.org/W6774713072","https://openalex.org/W6779141816","https://openalex.org/W6781810711","https://openalex.org/W6794679841","https://openalex.org/W6800961365","https://openalex.org/W6803860320","https://openalex.org/W6809946453","https://openalex.org/W6849731585","https://openalex.org/W6854072818"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W2390279801","https://openalex.org/W4391913857","https://openalex.org/W2358668433","https://openalex.org/W4396701345","https://openalex.org/W2376932109","https://openalex.org/W2001405890","https://openalex.org/W4396696052"],"abstract_inverted_index":{"This":[0,88],"paper":[1],"explores":[2],"stochastic":[3],"multi-level":[4],"compositional":[5],"optimization,":[6],"where":[7,190],"the":[8,41,49,56,73,78,91,109,118,150,155,187,193,209,215],"objective":[9],"function":[10,74],"is":[11],"a":[12,84,161],"composition":[13],"of":[14,60,125,131,163,195,203],"multiple":[15],"smooth":[16],"functions.":[17],"Traditional":[18],"methods":[19],"for":[20,69,98,106,167,175,184],"solving":[21],"this":[22],"problem":[23],"suffer":[24],"from":[25],"either":[26],"sub-optimal":[27],"sample":[28,58,92],"complexities":[29,116,217],"or":[30,77,112,135],"require":[31],"huge":[32],"batch":[33,143],"sizes.":[34],"To":[35,200],"address":[36],"these":[37],"limitations,":[38],"we":[39,82,153,207],"introduce":[40],"Stochastic":[42],"Multi-level":[43],"Variance":[44],"Reduction":[45],"(SMVR)":[46],"method.":[47],"In":[48],"expectation":[50],"case,":[51,152],"our":[52],"SMVR":[53,86,211],"method":[54],"attains":[55],"optimal":[57],"complexity":[59,93,162],"$\\mathcal":[61,95,102,164,170,179],"{O}(1/\\epsilon":[62,96],"^{3})$O(1/\u03b53)":[63],"to":[64,94],"find":[65],"an":[66],"$\\epsilon$\u03b5-stationary":[67],"point":[68],"non-convex":[70,168],"objectives.":[71],"When":[72],"satisfies":[75],"convexity":[76],"Polyak-\u0141ojasiewicz":[79],"(PL)":[80],"condition,":[81,189],"propose":[83,208],"stage-wise":[85],"variant.":[87],"variant":[89],"improves":[90],"^{2})$O(1/\u03b52)":[97],"convex":[99,137,176],"functions":[100,107,177,196],"and":[101,178],"{O}(1/(\\mu":[103],"\\epsilon":[104],"))$O(1/(\u03bc\u03b5))":[105],"meeting":[108],"$\\mu$\u03bc-PL":[110,188],"condition":[111],"$\\mu$\u03bc-strong":[113],"convexity.":[114],"These":[115],"match":[117],"lower":[119],"bounds":[120],"not":[121],"only":[122],"in":[123,129,145,149,197,222],"terms":[124,130],"$\\epsilon$\u03b5":[126],"but":[127],"also":[128],"$\\mu$\u03bc":[132],"(for":[133],"PL":[134],"strongly":[136],"functions),":[138],"without":[139],"relying":[140],"on":[141],"large":[142],"sizes":[144],"each":[146,198],"iteration.":[147],"Furthermore,":[148],"finite-sum":[151],"develop":[154],"SMVR-FS":[156],"algorithm,":[157],"which":[158,213],"can":[159],"achieve":[160],"{O}(\\sqrt{n}/\\epsilon":[165,171],"^{2})$O(n/\u03b52)":[166],"objectives,":[169],"\\log":[172,181],"(1/\\epsilon":[173,182],"))$O(n/\u03b5log(1/\u03b5))":[174],"{O}(\\sqrt{n}/\\mu":[180],"))$O(n/\u03bclog(1/\u03b5))":[183],"objectives":[185],"satisfying":[186],"$n$n":[191],"denotes":[192],"number":[194],"level.":[199],"make":[201],"use":[202],"adaptive":[204],"learning":[205],"rates,":[206],"Adaptive":[210],"method,":[212],"maintains":[214],"same":[216],"while":[218],"demonstrating":[219],"faster":[220],"convergence":[221],"practice.":[223]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2025-12-28T23:10:05.387466","created_date":"2025-10-10T00:00:00"}