{"id":"https://openalex.org/W4408564779","doi":"https://doi.org/10.1109/tnnls.2025.3545420","title":"Convergence of Adaptive Stochastic Mirror Descent","display_name":"Convergence of Adaptive Stochastic Mirror Descent","publication_year":2025,"publication_date":"2025-03-18","ids":{"openalex":"https://openalex.org/W4408564779","doi":"https://doi.org/10.1109/tnnls.2025.3545420","pmid":"https://pubmed.ncbi.nlm.nih.gov/40100666"},"language":"en","primary_location":{"id":"doi:10.1109/tnnls.2025.3545420","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnnls.2025.3545420","pdf_url":null,"source":{"id":"https://openalex.org/S4210175523","display_name":"IEEE Transactions on Neural Networks and Learning Systems","issn_l":"2162-237X","issn":["2162-237X","2162-2388"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["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 Neural Networks and Learning Systems","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/A5101806617","display_name":"Ting Hu","orcid":"https://orcid.org/0009-0009-9676-2854"},"institutions":[{"id":"https://openalex.org/I87445476","display_name":"Xi'an Jiaotong University","ror":"https://ror.org/017zhmm22","country_code":"CN","type":"education","lineage":["https://openalex.org/I87445476"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ting Hu","raw_affiliation_strings":["School of Management, Xi’an Jiaotong University, Xi’an, China"],"raw_orcid":"https://orcid.org/0009-0009-9676-2854","affiliations":[{"raw_affiliation_string":"School of Management, Xi’an Jiaotong University, Xi’an, China","institution_ids":["https://openalex.org/I87445476"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103161979","display_name":"Xiaotong Liu","orcid":"https://orcid.org/0009-0004-5928-5394"},"institutions":[{"id":"https://openalex.org/I87445476","display_name":"Xi'an Jiaotong University","ror":"https://ror.org/017zhmm22","country_code":"CN","type":"education","lineage":["https://openalex.org/I87445476"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiaotong Liu","raw_affiliation_strings":["School of Management, Xi’an Jiaotong University, Xi’an, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Management, Xi’an Jiaotong University, Xi’an, China","institution_ids":["https://openalex.org/I87445476"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5110854878","display_name":"Kai Ji","orcid":null},"institutions":[{"id":"https://openalex.org/I2250955327","display_name":"Huawei Technologies (China)","ror":"https://ror.org/00cmhce21","country_code":"CN","type":"company","lineage":["https://openalex.org/I2250955327"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Kai Ji","raw_affiliation_strings":["Huawei Technologies Company Ltd., Shenzhen, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Huawei Technologies Company Ltd., Shenzhen, China","institution_ids":["https://openalex.org/I2250955327"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5046468616","display_name":"Yunwen Lei","orcid":"https://orcid.org/0000-0002-5383-467X"},"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":"Yunwen Lei","raw_affiliation_strings":["Department of Mathematics, The University of Hong Kong, Hong Kong, China"],"raw_orcid":"https://orcid.org/0000-0002-5383-467X","affiliations":[{"raw_affiliation_string":"Department of Mathematics, The University of Hong Kong, Hong Kong, China","institution_ids":["https://openalex.org/I889458895"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.3936,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.74727143,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":97},"biblio":{"volume":"36","issue":"8","first_page":"14963","last_page":"14974"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.8842999935150146,"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.8842999935150146,"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/T10719","display_name":"3D Shape Modeling and Analysis","score":0.8622000217437744,"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/T12983","display_name":"Satellite Image Processing and Photogrammetry","score":0.8230000138282776,"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/convergence","display_name":"Convergence (economics)","score":0.7342235445976257},{"id":"https://openalex.org/keywords/descent","display_name":"Descent (aeronautics)","score":0.641233503818512},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5022690296173096},{"id":"https://openalex.org/keywords/stochastic-gradient-descent","display_name":"Stochastic gradient descent","score":0.47855621576309204},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3896440863609314},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3594440817832947},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.32830798625946045},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.18039748072624207},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.15464049577713013},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.11270639300346375},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.08804723620414734},{"id":"https://openalex.org/keywords/meteorology","display_name":"Meteorology","score":0.04596585035324097}],"concepts":[{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.7342235445976257},{"id":"https://openalex.org/C2776637919","wikidata":"https://www.wikidata.org/wiki/Q624380","display_name":"Descent (aeronautics)","level":2,"score":0.641233503818512},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5022690296173096},{"id":"https://openalex.org/C206688291","wikidata":"https://www.wikidata.org/wiki/Q7617819","display_name":"Stochastic gradient descent","level":3,"score":0.47855621576309204},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3896440863609314},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3594440817832947},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.32830798625946045},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.18039748072624207},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.15464049577713013},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.11270639300346375},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.08804723620414734},{"id":"https://openalex.org/C153294291","wikidata":"https://www.wikidata.org/wiki/Q25261","display_name":"Meteorology","level":1,"score":0.04596585035324097},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/tnnls.2025.3545420","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnnls.2025.3545420","pdf_url":null,"source":{"id":"https://openalex.org/S4210175523","display_name":"IEEE Transactions on Neural Networks and Learning Systems","issn_l":"2162-237X","issn":["2162-237X","2162-2388"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["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 Neural Networks and Learning Systems","raw_type":"journal-article"},{"id":"pmid:40100666","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/40100666","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 neural networks and learning systems","raw_type":null},{"id":"pmh:oai:hub.hku.hk:10722/357587","is_oa":false,"landing_page_url":"https://hub.hku.hk/handle/10722/357587","pdf_url":null,"source":{"id":"https://openalex.org/S4377196271","display_name":"The HKU Scholars Hub (University of Hong Kong)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I889458895","host_organization_name":"University of Hong Kong","host_organization_lineage":["https://openalex.org/I889458895"],"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":"Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3285408012","display_name":null,"funder_award_id":"12071356","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6973827008","display_name":null,"funder_award_id":"12471095","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7186889926","display_name":null,"funder_award_id":"22303723","funder_id":"https://openalex.org/F4320322887","funder_display_name":"The Research Council"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320322887","display_name":"The Research Council","ror":"https://ror.org/03tcppy59"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":53,"referenced_works":["https://openalex.org/W1551269584","https://openalex.org/W2005082281","https://openalex.org/W2016384870","https://openalex.org/W2016611950","https://openalex.org/W2046470130","https://openalex.org/W2090376964","https://openalex.org/W2112980792","https://openalex.org/W2116040458","https://openalex.org/W2169713291","https://openalex.org/W2551153860","https://openalex.org/W2578544862","https://openalex.org/W2803423166","https://openalex.org/W2803681939","https://openalex.org/W2904039766","https://openalex.org/W2911067482","https://openalex.org/W2963698657","https://openalex.org/W2964211254","https://openalex.org/W3017285694","https://openalex.org/W3020853991","https://openalex.org/W3034995656","https://openalex.org/W3090668255","https://openalex.org/W3096312061","https://openalex.org/W4293363567","https://openalex.org/W4401439238","https://openalex.org/W6605426635","https://openalex.org/W6631190155","https://openalex.org/W6681435938","https://openalex.org/W6681723013","https://openalex.org/W6738491991","https://openalex.org/W6746052068","https://openalex.org/W6747043858","https://openalex.org/W6747620207","https://openalex.org/W6748482152","https://openalex.org/W6751189704","https://openalex.org/W6753170497","https://openalex.org/W6754054930","https://openalex.org/W6754651742","https://openalex.org/W6754654111","https://openalex.org/W6755207826","https://openalex.org/W6755312952","https://openalex.org/W6755318316","https://openalex.org/W6757751764","https://openalex.org/W6778883912","https://openalex.org/W6780688020","https://openalex.org/W6784955064","https://openalex.org/W6793630500","https://openalex.org/W6799761402","https://openalex.org/W6805973258","https://openalex.org/W6809498554","https://openalex.org/W6852226950","https://openalex.org/W6858506742","https://openalex.org/W6861947122","https://openalex.org/W6871472795"],"related_works":["https://openalex.org/W2486267010","https://openalex.org/W4298096494","https://openalex.org/W1678820847","https://openalex.org/W2559216629","https://openalex.org/W1553684505","https://openalex.org/W1607707911","https://openalex.org/W2037211941","https://openalex.org/W2042403445","https://openalex.org/W2725816051","https://openalex.org/W2588465033"],"abstract_inverted_index":{"In":[0,54,102],"this":[1],"article,":[2],"we":[3,61],"present":[4],"a":[5,134],"family":[6,43],"of":[7,27,51,57,105,115,127,148,159],"adaptive":[8,35],"stochastic":[9],"optimization":[10,28],"methods,":[11],"which":[12],"are":[13,19,99,143],"associated":[14],"with":[15,64,145],"mirror":[16,46,120],"maps":[17,47],"that":[18,63,142],"widely":[20],"used":[21],"to":[22,92,133],"capture":[23],"the":[24,42,45,49,55,70,75,96,103,116,157,160],"geometry":[25],"properties":[26,114],"problems":[29],"during":[30],"iteration":[31],"processes.":[32],"The":[33],"well-known":[34],"moment":[36],"estimation":[37],"(Adam)-type":[38],"algorithm":[39],"falls":[40],"into":[41],"when":[44,95],"take":[48],"form":[50],"temporal":[52],"adaptation.":[53],"context":[56,104],"convex":[58,118],"objective":[59,97,107],"functions,":[60],"show":[62],"proper":[65],"step":[66],"sizes":[67],"and":[68],"hyperparameters,":[69],"average":[71],"regret":[72],"can":[73],"achieve":[74,124],"convergence":[76,125],"rate":[77],"${\\mathcal":[78,129],"{":[79,130],"O}}(T^{-(1/2)})$":[80,131],"after":[81],"T":[82],"iterations":[83],"under":[84],"some":[85],"standard":[86],"assumptions.":[87],"We":[88],"further":[89],"improve":[90],"it":[91],"$O(T^{-1}\\log":[93],"T)$":[94],"functions":[98,108],"strongly":[100,117],"convex.":[101],"smooth":[106],"(not":[109],"necessarily":[110],"convex),":[111],"based":[112],"on":[113],"differentiable":[119],"map,":[121],"our":[122,152],"algorithms":[123],"rates":[126],"order":[128],"up":[132],"logarithmic":[135],"term,":[136],"requiring":[137],"large":[138],"or":[139],"increasing":[140],"hyperparameters":[141,161],"coincident":[144],"practical":[146],"usage":[147],"Adam-type":[149,163],"algorithms.":[150],"Thus,":[151],"work":[153],"gives":[154],"explanations":[155],"for":[156],"selection":[158],"in":[162],"algorithms'":[164],"implementation.":[165]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1}],"updated_date":"2026-07-15T18:14:33.161393","created_date":"2025-10-10T00:00:00"}