{"id":"https://openalex.org/W4205293988","doi":"https://doi.org/10.1109/tpami.2022.3140249","title":"A General Descent Aggregation Framework for Gradient-Based Bi-Level Optimization","display_name":"A General Descent Aggregation Framework for Gradient-Based Bi-Level Optimization","publication_year":2022,"publication_date":"2022-01-04","ids":{"openalex":"https://openalex.org/W4205293988","doi":"https://doi.org/10.1109/tpami.2022.3140249","pmid":"https://pubmed.ncbi.nlm.nih.gov/34982677"},"language":"en","primary_location":{"id":"doi:10.1109/tpami.2022.3140249","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tpami.2022.3140249","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":"https://openalex.org/A5042370642","display_name":"Risheng Liu","orcid":"https://orcid.org/0000-0002-9554-0565"},"institutions":[{"id":"https://openalex.org/I27357992","display_name":"Dalian University of Technology","ror":"https://ror.org/023hj5876","country_code":"CN","type":"education","lineage":["https://openalex.org/I27357992"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Risheng Liu","raw_affiliation_strings":["DUT-RU International School of Information Science &#x0026; Engineering, Dalian University of Technology, Dalian, China"],"affiliations":[{"raw_affiliation_string":"DUT-RU International School of Information Science &#x0026; Engineering, Dalian University of Technology, Dalian, China","institution_ids":["https://openalex.org/I27357992"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5006040955","display_name":"Pan Mu","orcid":"https://orcid.org/0000-0002-5330-2673"},"institutions":[{"id":"https://openalex.org/I27357992","display_name":"Dalian University of Technology","ror":"https://ror.org/023hj5876","country_code":"CN","type":"education","lineage":["https://openalex.org/I27357992"]},{"id":"https://openalex.org/I55712492","display_name":"Zhejiang University of Technology","ror":"https://ror.org/02djqfd08","country_code":"CN","type":"education","lineage":["https://openalex.org/I55712492"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Pan Mu","raw_affiliation_strings":["College of Computer Science and Technology, Zhejiang University of Technology, Hangzhou, China","School of Mathematical Sciences, Dalian University of Technology, Dalian, China"],"affiliations":[{"raw_affiliation_string":"College of Computer Science and Technology, Zhejiang University of Technology, Hangzhou, China","institution_ids":["https://openalex.org/I55712492"]},{"raw_affiliation_string":"School of Mathematical Sciences, Dalian University of Technology, Dalian, China","institution_ids":["https://openalex.org/I27357992"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5060269704","display_name":"Xiaoming Yuan","orcid":"https://orcid.org/0000-0002-6900-6983"},"institutions":[{"id":"https://openalex.org/I889458895","display_name":"University of Hong Kong","ror":"https://ror.org/02zhqgq86","country_code":"HK","type":"education","lineage":["https://openalex.org/I889458895"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Xiaoming Yuan","raw_affiliation_strings":["Department of Mathematics, The University of Hong Kong, Hong Kang, China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, The University of Hong Kong, Hong Kang, China","institution_ids":["https://openalex.org/I889458895"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5014555178","display_name":"Shangzhi Zeng","orcid":"https://orcid.org/0000-0002-6950-7825"},"institutions":[{"id":"https://openalex.org/I212119943","display_name":"University of Victoria","ror":"https://ror.org/04s5mat29","country_code":"CA","type":"education","lineage":["https://openalex.org/I212119943"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Shangzhi Zeng","raw_affiliation_strings":["Department of Mathematics and Statistics, University of Victoria, Victoria, BC, Canada"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, University of Victoria, Victoria, BC, Canada","institution_ids":["https://openalex.org/I212119943"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5080552363","display_name":"Jin Zhang","orcid":"https://orcid.org/0000-0002-6691-5612"},"institutions":[{"id":"https://openalex.org/I3045169105","display_name":"Southern University of Science and Technology","ror":"https://ror.org/049tv2d57","country_code":"CN","type":"education","lineage":["https://openalex.org/I3045169105"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jin Zhang","raw_affiliation_strings":["Department of Mathematics, SUSTech International Center for Mathematics, National Center for Applied Mathematics Shenzhen, Southern University of Science and Technology, Shenzhen, Guangdong, China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, SUSTech International Center for Mathematics, National Center for Applied Mathematics Shenzhen, Southern University of Science and Technology, Shenzhen, Guangdong, China","institution_ids":["https://openalex.org/I3045169105"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5042370642"],"corresponding_institution_ids":["https://openalex.org/I27357992"],"apc_list":null,"apc_paid":null,"fwci":4.2965,"has_fulltext":false,"cited_by_count":28,"citation_normalized_percentile":{"value":0.95421598,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"45","issue":"1","first_page":"38","last_page":"57"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9998999834060669,"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"}},{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9973000288009644,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9973000288009644,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.7363020777702332},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.7023239135742188},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.7013502717018127},{"id":"https://openalex.org/keywords/correctness","display_name":"Correctness","score":0.6609808802604675},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5753887891769409},{"id":"https://openalex.org/keywords/descent","display_name":"Descent (aeronautics)","score":0.46068906784057617},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.45840221643447876},{"id":"https://openalex.org/keywords/stochastic-gradient-descent","display_name":"Stochastic gradient descent","score":0.4578700065612793},{"id":"https://openalex.org/keywords/code","display_name":"Code (set theory)","score":0.43623924255371094},{"id":"https://openalex.org/keywords/aggregate","display_name":"Aggregate (composite)","score":0.42158204317092896},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.34929904341697693},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3224320411682129},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3168071508407593},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.19609573483467102},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.07784664630889893}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7363020777702332},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.7023239135742188},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.7013502717018127},{"id":"https://openalex.org/C55439883","wikidata":"https://www.wikidata.org/wiki/Q360812","display_name":"Correctness","level":2,"score":0.6609808802604675},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5753887891769409},{"id":"https://openalex.org/C2776637919","wikidata":"https://www.wikidata.org/wiki/Q624380","display_name":"Descent (aeronautics)","level":2,"score":0.46068906784057617},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.45840221643447876},{"id":"https://openalex.org/C206688291","wikidata":"https://www.wikidata.org/wiki/Q7617819","display_name":"Stochastic gradient descent","level":3,"score":0.4578700065612793},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.43623924255371094},{"id":"https://openalex.org/C4679612","wikidata":"https://www.wikidata.org/wiki/Q866298","display_name":"Aggregate (composite)","level":2,"score":0.42158204317092896},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.34929904341697693},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3224320411682129},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3168071508407593},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.19609573483467102},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.07784664630889893},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tpami.2022.3140249","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tpami.2022.3140249","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:34982677","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/34982677","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/G3049148066","display_name":null,"funder_award_id":"11971220","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8944108821","display_name":null,"funder_award_id":"61922019","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320310984","display_name":"Pacific Institute for the Mathematical Sciences","ror":"https://ror.org/04w49dw51"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320335787","display_name":"Fundamental Research Funds for the Central Universities","ror":null},{"id":"https://openalex.org/F4320337111","display_name":"Basic and Applied Basic Research Foundation of Guangdong Province","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":77,"referenced_works":["https://openalex.org/W1868018859","https://openalex.org/W1916477561","https://openalex.org/W1970163214","https://openalex.org/W2019613464","https://openalex.org/W2023858465","https://openalex.org/W2053072311","https://openalex.org/W2064997474","https://openalex.org/W2112796928","https://openalex.org/W2157590940","https://openalex.org/W2194321275","https://openalex.org/W2270245739","https://openalex.org/W2600297185","https://openalex.org/W2604763608","https://openalex.org/W2625674597","https://openalex.org/W2742093937","https://openalex.org/W2750384547","https://openalex.org/W2763081248","https://openalex.org/W2786022758","https://openalex.org/W2806987515","https://openalex.org/W2914953695","https://openalex.org/W2950728319","https://openalex.org/W2951104886","https://openalex.org/W2962708927","https://openalex.org/W2962727772","https://openalex.org/W2963341924","https://openalex.org/W2963938169","https://openalex.org/W2967733054","https://openalex.org/W2970005388","https://openalex.org/W2970161765","https://openalex.org/W2972954809","https://openalex.org/W2980342893","https://openalex.org/W3005761507","https://openalex.org/W3007846651","https://openalex.org/W3033095513","https://openalex.org/W3034466185","https://openalex.org/W3035016095","https://openalex.org/W3089944207","https://openalex.org/W3098015273","https://openalex.org/W3101372274","https://openalex.org/W3108326355","https://openalex.org/W3170557719","https://openalex.org/W3202650012","https://openalex.org/W4226468895","https://openalex.org/W4229650096","https://openalex.org/W4287750664","https://openalex.org/W4288027470","https://openalex.org/W4294646197","https://openalex.org/W4295292688","https://openalex.org/W4297800546","https://openalex.org/W4297803541","https://openalex.org/W4301014524","https://openalex.org/W6638908295","https://openalex.org/W6639506587","https://openalex.org/W6693919493","https://openalex.org/W6717697761","https://openalex.org/W6734265508","https://openalex.org/W6736057607","https://openalex.org/W6742288159","https://openalex.org/W6743688258","https://openalex.org/W6748567128","https://openalex.org/W6750254146","https://openalex.org/W6751797489","https://openalex.org/W6751962046","https://openalex.org/W6752515464","https://openalex.org/W6755905128","https://openalex.org/W6757297395","https://openalex.org/W6767019922","https://openalex.org/W6767067800","https://openalex.org/W6767599400","https://openalex.org/W6770070843","https://openalex.org/W6774288828","https://openalex.org/W6778983485","https://openalex.org/W6779138978","https://openalex.org/W6780106526","https://openalex.org/W6796849125","https://openalex.org/W6802312262","https://openalex.org/W6810887272"],"related_works":["https://openalex.org/W4206903459","https://openalex.org/W2754816816","https://openalex.org/W4366280654","https://openalex.org/W3160167280","https://openalex.org/W4231621013","https://openalex.org/W4362706668","https://openalex.org/W2015288657","https://openalex.org/W3008318776","https://openalex.org/W1977633006","https://openalex.org/W2041416246"],"abstract_inverted_index":{"In":[0,81],"recent":[1],"years,":[2],"a":[3,68,94,113,134,141],"variety":[4],"of":[5,31,77,151,163,192],"gradient-based":[6,79,96,152],"methods":[7],"have":[8],"been":[9],"developed":[10],"to":[11,71,104,116,125,145],"solve":[12],"Bi-Level":[13],"Optimization":[14],"(BLO)":[15],"problems":[16],"in":[17,50,165],"machine":[18],"learning":[19],"and":[20,28,92,122,139,188,199],"computer":[21],"vision":[22],"areas.":[23],"However,":[24],"the":[25,74,107,120,147,160,190,193],"theoretical":[26,58,149,186],"correctness":[27],"practical":[29],"effectiveness":[30],"these":[32],"existing":[33],"approaches":[34],"always":[35],"rely":[36],"on":[37,61],"some":[38],"restrictive":[39],"conditions":[40],"(e.g.,":[41],"Lower-Level":[42],"Singleton,":[43],"LLS),":[44],"which":[45],"could":[46],"hardly":[47],"be":[48],"satisfied":[49],"real-world":[51],"applications.":[52],"Moreover,":[53],"previous":[54],"literature":[55],"only":[56],"proves":[57],"results":[59,187],"based":[60],"their":[62],"specific":[63],"iteration":[64],"strategies,":[65],"thus":[66],"lack":[67],"general":[69,135],"recipe":[70,144],"uniformly":[72],"analyze":[73],"convergence":[75,136,161],"behaviors":[76],"different":[78,166],"BLOs.":[80],"this":[82,156],"work,":[83],"we":[84,132],"formulate":[85],"BLOs":[86],"from":[87,178],"an":[88],"optimistic":[89],"bi-level":[90,128],"viewpoint":[91],"establish":[93,133],"new":[95,142],"algorithmic":[97],"framework,":[98],"named":[99],"Bi-level":[100],"Descent":[101],"Aggregation":[102],"(BDA),":[103],"partially":[105],"address":[106],"above":[108],"issues.":[109],"Specifically,":[110],"BDA":[111,164],"provides":[112],"modularized":[114],"structure":[115],"hierarchically":[117],"aggregate":[118],"both":[119],"upper-":[121],"lower-level":[123],"subproblems":[124],"generate":[126],"our":[127,185],"iterative":[129],"dynamics.":[130],"Theoretically,":[131],"analysis":[137],"template":[138],"derive":[140],"proof":[143],"investigate":[146],"essential":[148],"properties":[150],"BLO":[153],"methods.":[154],"Furthermore,":[155],"work":[157],"systematically":[158],"explores":[159],"behavior":[162],"optimization":[167,198],"scenarios,":[168],"i.e.,":[169],"considering":[170],"various":[171],"solution":[172],"qualities":[173],"(i.e.,":[174],"global/local/stationary":[175],"solution)":[176],"returned":[177],"solving":[179],"approximation":[180],"subproblems.":[181],"Extensive":[182],"experiments":[183],"justify":[184],"demonstrate":[189],"superiority":[191],"proposed":[194],"algorithm":[195],"for":[196],"hyper-parameter":[197],"meta-learning":[200],"tasks.":[201],"Source":[202],"code":[203],"is":[204],"available":[205],"at":[206],"https://github.com/vis-opt-group/BDA.":[207]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":8},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":9},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":1}],"updated_date":"2026-03-09T08:58:05.943551","created_date":"2025-10-10T00:00:00"}
