{"id":"https://openalex.org/W2804529069","doi":"https://doi.org/10.48550/arxiv.1806.04910","title":"Bilevel Programming for Hyperparameter Optimization and Meta-Learning","display_name":"Bilevel Programming for Hyperparameter Optimization and Meta-Learning","publication_year":2018,"publication_date":"2018-06-13","ids":{"openalex":"https://openalex.org/W2804529069","doi":"https://doi.org/10.48550/arxiv.1806.04910","mag":"2804529069"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:1806.04910","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1806.04910","pdf_url":"https://arxiv.org/pdf/1806.04910","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1806.04910","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5074874504","display_name":"Luca Franceschi","orcid":"https://orcid.org/0000-0002-1810-1016","observed_orcids":["https://orcid.org/0000-0002-1810-1016"]},"institutions":[{"id":"https://openalex.org/I30771326","display_name":"Italian Institute of Technology","ror":"https://ror.org/042t93s57","country_code":"IT","type":"facility","lineage":["https://openalex.org/I30771326"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Franceschi, Luca","raw_affiliation_strings":["Italian Institute of Technology, Genoa, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Italian Institute of Technology, Genoa, Italy","institution_ids":["https://openalex.org/I30771326"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5027422071","display_name":"Paolo Frasconi","orcid":"https://orcid.org/0000-0003-3117-9245","observed_orcids":["https://orcid.org/0000-0003-3117-9245"]},"institutions":[{"id":"https://openalex.org/I45084792","display_name":"University of Florence","ror":"https://ror.org/04jr1s763","country_code":"IT","type":"education","lineage":["https://openalex.org/I45084792"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Frasconi, Paolo","raw_affiliation_strings":["University of Florence, Florence, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Florence, Florence, Italy","institution_ids":["https://openalex.org/I45084792"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5017463552","display_name":"Saverio Salzo","orcid":"https://orcid.org/0000-0003-0494-9101","observed_orcids":["https://orcid.org/0000-0003-0494-9101"]},"institutions":[{"id":"https://openalex.org/I30771326","display_name":"Italian Institute of Technology","ror":"https://ror.org/042t93s57","country_code":"IT","type":"facility","lineage":["https://openalex.org/I30771326"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Salzo, Saverio","raw_affiliation_strings":["Italian Institute of Technology, Genoa, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Italian Institute of Technology, Genoa, Italy","institution_ids":["https://openalex.org/I30771326"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5034665821","display_name":"Riccardo Grazzi","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I30771326","display_name":"Italian Institute of Technology","ror":"https://ror.org/042t93s57","country_code":"IT","type":"facility","lineage":["https://openalex.org/I30771326"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Grazzi, Riccardo","raw_affiliation_strings":["Italian Institute of Technology, Genoa, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Italian Institute of Technology, Genoa, Italy","institution_ids":["https://openalex.org/I30771326"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5086180934","display_name":"Massimilano Pontil","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I30771326","display_name":"Italian Institute of Technology","ror":"https://ror.org/042t93s57","country_code":"IT","type":"facility","lineage":["https://openalex.org/I30771326"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Pontil, Massimilano","raw_affiliation_strings":["Italian Institute of Technology, Genoa, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Italian Institute of Technology, Genoa, Italy","institution_ids":["https://openalex.org/I30771326"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":308,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":"80","issue":null,"first_page":"1568","last_page":"1577"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11307","display_name":"Domain Adaptation and Few-Shot Learning","score":0.86080002784729,"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/T11307","display_name":"Domain Adaptation and Few-Shot Learning","score":0.86080002784729,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.08219999819993973,"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/T12535","display_name":"Machine Learning and Data Classification","score":0.04529999941587448,"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/bi-level-optimization","display_name":"bi-level optimization","score":0.9319999814033508},{"id":"https://openalex.org/keywords/hyperparameter-optimization","display_name":"hyperparameter optimization","score":0.9959999918937683},{"id":"https://openalex.org/keywords/meta-learning","display_name":"meta-learning","score":0.9829999804496765},{"id":"https://openalex.org/keywords/convergence-analysis","display_name":"convergence analysis","score":0.6930000185966492},{"id":"https://openalex.org/keywords/few-shot-learning","display_name":"few-shot learning","score":0.7390000224113464}],"concepts":[{"id":"https://openalex.org/C8642999","wikidata":"https://www.wikidata.org/wiki/Q4171168","display_name":"Hyperparameter","level":2,"score":0.9591454267501831},{"id":"https://openalex.org/C3309286","wikidata":"https://www.wikidata.org/wiki/Q4907693","display_name":"Bilevel optimization","level":3,"score":0.8690854907035828},{"id":"https://openalex.org/C2781002164","wikidata":"https://www.wikidata.org/wiki/Q6822311","display_name":"Meta learning (computer science)","level":3,"score":0.7458118796348572},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6328227519989014},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.6179303526878357},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.5559139251708984},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5403814911842346},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.5322636961936951},{"id":"https://openalex.org/C10485038","wikidata":"https://www.wikidata.org/wiki/Q48996162","display_name":"Hyperparameter optimization","level":3,"score":0.4432280659675598},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.39126986265182495},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.3896976113319397},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2040829360485077},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.19597983360290527},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C2780451532","wikidata":"https://www.wikidata.org/wiki/Q759676","display_name":"Task (project management)","level":2,"score":0.0},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0},{"id":"https://openalex.org/C12267149","wikidata":"https://www.wikidata.org/wiki/Q282453","display_name":"Support vector machine","level":2,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"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/C187736073","wikidata":"https://www.wikidata.org/wiki/Q2920921","display_name":"Management","level":1,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"pmh:oai:arXiv.org:1806.04910","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1806.04910","pdf_url":"https://arxiv.org/pdf/1806.04910","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"mag:2804529069","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1806.04910","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:eprints.ucl.ac.uk.OAI2:10073436","doi":null,"is_oa":false,"landing_page_url":"https://discovery.ucl.ac.uk/id/eprint/10073436/","pdf_url":null,"source":{"id":"https://openalex.org/S4306400024","display_name":"UCL Discovery (University College London)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I45129253","host_organization_name":"University College London","host_organization_lineage":["https://openalex.org/I45129253"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"In: Dy, JG and Krause, A, (eds.) Proceedings of the 25th International Conference on Machine Learning (2018). (pp. pp. 1563-1572). PMLR (Proceedings of Machine Learning Research): Stockholm. (2018)","raw_type":"Proceedings paper"},{"id":"pmh:oai:flore.unifi.it:2158/1150954","doi":null,"is_oa":true,"landing_page_url":"http://hdl.handle.net/2158/1150954","pdf_url":null,"source":{"id":"https://openalex.org/S4306402033","display_name":"Florence Research (University of Florence)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I45084792","host_organization_name":"University of Florence","host_organization_lineage":["https://openalex.org/I45084792"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/conferenceObject"},{"id":"doi:10.48550/arxiv.1806.04910","doi":"https://doi.org/10.48550/arxiv.1806.04910","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1806.04910","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":false,"raw_source_name":null,"raw_type":"Preprint"},{"id":"mag:2963306862","doi":null,"is_oa":false,"landing_page_url":"http://proceedings.mlr.press/v80/franceschi18a/franceschi18a.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306419644","display_name":"International Conference on Machine Learning","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"conference"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":"International Conference on Machine Learning","raw_type":null}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1806.04910","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1806.04910","pdf_url":"https://arxiv.org/pdf/1806.04910","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2804529069.pdf","grobid_xml":"https://content.openalex.org/works/W2804529069.grobid-xml"},"referenced_works_count":37,"referenced_works":["https://openalex.org/W99485931","https://openalex.org/W1533861849","https://openalex.org/W1585773866","https://openalex.org/W1852255964","https://openalex.org/W1868018859","https://openalex.org/W2089217417","https://openalex.org/W2108598243","https://openalex.org/W2113207845","https://openalex.org/W2124022122","https://openalex.org/W2131241448","https://openalex.org/W2144752499","https://openalex.org/W2166344886","https://openalex.org/W2187061624","https://openalex.org/W2194321275","https://openalex.org/W2194775991","https://openalex.org/W2210969396","https://openalex.org/W2270245739","https://openalex.org/W2328078142","https://openalex.org/W2412589713","https://openalex.org/W2427497464","https://openalex.org/W2432717477","https://openalex.org/W2583010282","https://openalex.org/W2594830834","https://openalex.org/W2601450892","https://openalex.org/W2604763608","https://openalex.org/W2626778328","https://openalex.org/W2753160622","https://openalex.org/W2787501667","https://openalex.org/W2790068046","https://openalex.org/W2914746235","https://openalex.org/W2951634833","https://openalex.org/W2962727772","https://openalex.org/W2963306862","https://openalex.org/W2964328735","https://openalex.org/W3037856073","https://openalex.org/W3091905774","https://openalex.org/W3122943284"],"related_works":["https://openalex.org/W3213473288","https://openalex.org/W2808123587","https://openalex.org/W2781376346","https://openalex.org/W4394635438","https://openalex.org/W3175433886","https://openalex.org/W4387165403","https://openalex.org/W4409364551","https://openalex.org/W4293352244","https://openalex.org/W4288055373","https://openalex.org/W3044569448"],"abstract_inverted_index":{"We":[0,15,64,82],"introduce":[1],"a":[2,55,62,103],"framework":[3],"based":[4],"on":[5,41],"bilevel":[6,23,124],"programming":[7],"that":[8,17],"unifies":[9],"gradient-based":[10],"hyperparameter":[11],"optimization":[12,34],"and":[13,121],"meta-learning.":[14],"show":[16],"an":[18],"approximate":[19,73],"version":[20],"of":[21,52,61,71,78,91,105],"the":[22,33,37,42,45,50,72,79,89,123],"problem":[24,58,74],"can":[25],"be":[26],"solved":[27],"by":[28],"taking":[29],"into":[30],"explicit":[31],"account":[32],"dynamics":[35],"for":[36,86,118,129],"inner":[38],"objective.":[39],"Depending":[40],"specific":[43],"setting,":[44],"outer":[46],"variables":[47],"take":[48],"either":[49],"meaning":[51],"hyperparameters":[53,100],"in":[54,88],"supervised":[56],"learning":[57,93,120],"or":[59],"parameters":[60],"meta-learner.":[63],"provide":[65],"sufficient":[66],"conditions":[67],"under":[68],"which":[69],"solutions":[70],"converge":[75],"to":[76],"those":[77],"exact":[80],"problem.":[81],"instantiate":[83],"our":[84,112],"approach":[85,125],"meta-learning":[87],"case":[90],"deep":[92],"where":[94],"representation":[95],"layers":[96],"are":[97],"treated":[98],"as":[99],"shared":[101],"across":[102],"set":[104],"training":[106],"episodes.":[107],"In":[108],"experiments,":[109],"we":[110],"confirm":[111],"theoretical":[113],"findings,":[114],"present":[115],"encouraging":[116],"results":[117],"few-shot":[119],"contrast":[122],"against":[126],"classical":[127],"approaches":[128],"learning-to-learn.":[130]},"counts_by_year":[{"year":2026,"cited_by_count":9},{"year":2025,"cited_by_count":26},{"year":2024,"cited_by_count":57},{"year":2023,"cited_by_count":60},{"year":2022,"cited_by_count":45},{"year":2021,"cited_by_count":45},{"year":2020,"cited_by_count":51},{"year":2019,"cited_by_count":12},{"year":2018,"cited_by_count":3}],"updated_date":"2026-11-10T11:39:43.021295","created_date":"2018-06-01T00:00:00"}
