{"id":"https://openalex.org/W4417427003","doi":"https://doi.org/10.1109/tpami.2025.3644443","title":"Augmenting Iterative Trajectory for Bilevel Optimization: Methodology, Analysis and Extensions","display_name":"Augmenting Iterative Trajectory for Bilevel Optimization: Methodology, Analysis and Extensions","publication_year":2025,"publication_date":"2025-12-15","ids":{"openalex":"https://openalex.org/W4417427003","doi":"https://doi.org/10.1109/tpami.2025.3644443","pmid":"https://pubmed.ncbi.nlm.nih.gov/41396772"},"language":"en","primary_location":{"id":"doi:10.1109/tpami.2025.3644443","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tpami.2025.3644443","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":["School of Software, Dalian University of Technology, Dalian, China"],"affiliations":[{"raw_affiliation_string":"School of Software, Dalian University of Technology, Dalian, China","institution_ids":["https://openalex.org/I27357992"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100674172","display_name":"Yaohua Liu","orcid":"https://orcid.org/0000-0002-5867-5065"},"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":"Yaohua Liu","raw_affiliation_strings":["School of Computing and Data Science, University of Hong Kong, Hong Kong, SAR, China"],"affiliations":[{"raw_affiliation_string":"School of Computing and Data Science, University of Hong Kong, Hong Kong, SAR, 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/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":"Shangzhi Zeng","raw_affiliation_strings":["National Center for Applied Mathematics, and Department of Mathematics, Southern University of Science and Technology, Shenzhen, China"],"affiliations":[{"raw_affiliation_string":"National Center for Applied Mathematics, and Department of Mathematics, Southern University of Science and Technology, Shenzhen, China","institution_ids":["https://openalex.org/I3045169105"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101533110","display_name":"Jin Zhang","orcid":"https://orcid.org/0000-0002-3285-8947"},"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, Southern University of Science and Technology, and National Center for Applied Mathematics, Shenzhen, China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Southern University of Science and Technology, and National Center for Applied Mathematics, Shenzhen, China","institution_ids":["https://openalex.org/I3045169105"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5042370642"],"corresponding_institution_ids":["https://openalex.org/I27357992"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.22421949,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"48","issue":"4","first_page":"4239","last_page":"4256"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9232000112533569,"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":0.9232000112533569,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.019700000062584877,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.011099999770522118,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/initialization","display_name":"Initialization","score":0.8428999781608582},{"id":"https://openalex.org/keywords/trajectory","display_name":"Trajectory","score":0.7174000144004822},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6513000130653381},{"id":"https://openalex.org/keywords/iterative-learning-control","display_name":"Iterative learning control","score":0.5989999771118164},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.579200029373169},{"id":"https://openalex.org/keywords/acceleration","display_name":"Acceleration","score":0.4819999933242798},{"id":"https://openalex.org/keywords/construct","display_name":"Construct (python library)","score":0.4172999858856201}],"concepts":[{"id":"https://openalex.org/C114466953","wikidata":"https://www.wikidata.org/wiki/Q6034165","display_name":"Initialization","level":2,"score":0.8428999781608582},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7263000011444092},{"id":"https://openalex.org/C13662910","wikidata":"https://www.wikidata.org/wiki/Q193139","display_name":"Trajectory","level":2,"score":0.7174000144004822},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6513000130653381},{"id":"https://openalex.org/C117619785","wikidata":"https://www.wikidata.org/wiki/Q6094414","display_name":"Iterative learning control","level":3,"score":0.5989999771118164},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.579200029373169},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4918000102043152},{"id":"https://openalex.org/C117896860","wikidata":"https://www.wikidata.org/wiki/Q11376","display_name":"Acceleration","level":2,"score":0.4819999933242798},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.4490000009536743},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.4172999858856201},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3578000068664551},{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.3483999967575073},{"id":"https://openalex.org/C106195933","wikidata":"https://www.wikidata.org/wiki/Q7847935","display_name":"Truncation (statistics)","level":2,"score":0.3422999978065491},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.34049999713897705},{"id":"https://openalex.org/C173246807","wikidata":"https://www.wikidata.org/wiki/Q7833062","display_name":"Trajectory optimization","level":3,"score":0.32199999690055847},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.2944999933242798},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.2786000072956085},{"id":"https://openalex.org/C2779982483","wikidata":"https://www.wikidata.org/wiki/Q6094420","display_name":"Iterative refinement","level":2,"score":0.2734000086784363},{"id":"https://openalex.org/C67186912","wikidata":"https://www.wikidata.org/wiki/Q367664","display_name":"Data modeling","level":2,"score":0.2538999915122986}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tpami.2025.3644443","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tpami.2025.3644443","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:41396772","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/41396772","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":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W1987083649","https://openalex.org/W2100556411","https://openalex.org/W2112796928","https://openalex.org/W2763081248","https://openalex.org/W2960010704","https://openalex.org/W2967733054","https://openalex.org/W2981748264","https://openalex.org/W2997072274","https://openalex.org/W3096831136","https://openalex.org/W3107893198","https://openalex.org/W3108326355","https://openalex.org/W3118521211","https://openalex.org/W3123350987","https://openalex.org/W4205293988","https://openalex.org/W4249513058","https://openalex.org/W4317897806","https://openalex.org/W4385656497","https://openalex.org/W7133201694"],"related_works":[],"abstract_inverted_index":{"In":[0,64],"recent":[1],"years,":[2],"there":[3],"has":[4],"been":[5],"a":[6],"surge":[7],"of":[8,85,171],"machine":[9],"learning":[10,178],"applications":[11,181],"developed":[12],"with":[13,51,162],"hierarchical":[14],"structure,":[15],"which":[16,55],"can":[17],"be":[18],"approached":[19],"from":[20],"Bi-Level":[21],"Optimization":[22],"(BLO)":[23],"perspective.":[24],"However,":[25],"most":[26],"existing":[27],"gradient-based":[28],"methods":[29],"overlook":[30],"the":[31,44,70,157,169],"interdependence":[32],"between":[33],"hyper-gradient":[34,89],"calculation":[35],"and":[36,74,82,104,109,122,138,148,155,179,185,188],"Lower-Level":[37],"(LL)":[38],"iterative":[39,72,119],"trajectory,":[40,73],"focusing":[41],"solely":[42],"on":[43],"former.":[45],"Consequently,":[46],"convergence":[47,144,158],"theory":[48],"is":[49],"constructed":[50,71],"restrictive":[52],"LL":[53,136,139,153,164],"assumptions,":[54,154],"are":[56],"often":[57],"challenging":[58,190],"to":[59,125],"satisfy":[60],"in":[61],"real-world":[62],"scenarios.":[63],"this":[65],"work,":[66],"we":[67,95,142,167],"thoroughly":[68],"analyze":[69],"highlight":[75],"two":[76,97],"deficiencies,":[77],"including":[78,100],"empirically":[79],"chosen":[80],"initialization":[81],"default":[83],"use":[84],"entire":[86],"trajectory":[87],"for":[88,131,146,160],"calculation.":[90],"To":[91],"address":[92],"these":[93],"issues,":[94],"introduce":[96],"augmentation":[98],"techniques":[99],"Initialization":[101],"Auxiliary":[102],"(IA)":[103],"Pessimistic":[105],"Trajectory":[106,129],"Truncation":[107],"(PTT),":[108],"investigate":[110],"various":[111],"extension":[112],"strategies":[113],"such":[114,192],"as":[115,193],"prior":[116],"regularization,":[117],"different":[118,152],"mapping":[120],"schemes":[121],"acceleration":[123],"dynamics":[124],"construct":[126],"Augmented":[127],"Iterative":[128],"(AIT)":[130],"corresponding":[132],"BLO":[133],"scenarios":[134],"(e.g.,":[135,182],"convexity":[137],"non-convexity).":[140],"Theoretically,":[141],"provide":[143],"analysis":[145,159],"AIT":[147,172],"its":[149],"variations":[150],"under":[151],"establish":[156],"BLOs":[161],"non-convex":[163],"subproblem.":[165],"Finally,":[166],"demonstrate":[168],"effectiveness":[170],"through":[173],"three":[174],"numerical":[175],"examples,":[176],"typical":[177],"vision":[180],"data":[183],"hyper-cleaning":[184],"few-shot":[186],"learning)":[187],"more":[189],"tasks":[191],"neural":[194],"architecture":[195],"search.":[196]},"counts_by_year":[],"updated_date":"2026-03-09T07:00:12.390032","created_date":"2025-12-15T00:00:00"}