{"id":"https://openalex.org/W4411142279","doi":"https://doi.org/10.1090/mcom/4103","title":"Gradient descent for convex and smooth noisy optimization","display_name":"Gradient descent for convex and smooth noisy optimization","publication_year":2025,"publication_date":"2025-06-09","ids":{"openalex":"https://openalex.org/W4411142279","doi":"https://doi.org/10.1090/mcom/4103"},"language":"lv","primary_location":{"id":"doi:10.1090/mcom/4103","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/4103","pdf_url":null,"source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"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/A5022816025","display_name":"Fang Q. Hu","orcid":"https://orcid.org/0009-0006-3076-9103"},"institutions":[{"id":"https://openalex.org/I36234482","display_name":"University of Bristol","ror":"https://ror.org/0524sp257","country_code":"GB","type":"education","lineage":["https://openalex.org/I36234482"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Feifei Hu","raw_affiliation_strings":["School of Mathematics, University of Bristol, Fry Building, Woodland Road, Bristol, BS8 1UG, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, University of Bristol, Fry Building, Woodland Road, Bristol, BS8 1UG, UK","institution_ids":["https://openalex.org/I36234482"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5021474812","display_name":"Mathieu Gerber","orcid":"https://orcid.org/0000-0001-6774-2330"},"institutions":[{"id":"https://openalex.org/I36234482","display_name":"University of Bristol","ror":"https://ror.org/0524sp257","country_code":"GB","type":"education","lineage":["https://openalex.org/I36234482"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Mathieu Gerber","raw_affiliation_strings":["School of Mathematics, University of Bristol, Fry Building, Woodland Road, Bristol, BS8 1UG, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, University of Bristol, Fry Building, Woodland Road, Bristol, BS8 1UG, UK","institution_ids":["https://openalex.org/I36234482"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I36234482"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.09456648,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"95","issue":"360","first_page":"1887","last_page":"1925"},"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9998999834060669,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9983000159263611,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8363784551620483},{"id":"https://openalex.org/keywords/descent","display_name":"Descent (aeronautics)","score":0.5955060720443726},{"id":"https://openalex.org/keywords/proximal-gradient-methods","display_name":"Proximal Gradient Methods","score":0.5842746496200562},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5576305389404297},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.5449283719062805},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.4796474575996399},{"id":"https://openalex.org/keywords/stochastic-gradient-descent","display_name":"Stochastic gradient descent","score":0.4361156225204468},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.41793322563171387},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3853724002838135},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.37535402178764343},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.26157695055007935},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.15134993195533752},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.10531109571456909}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8363784551620483},{"id":"https://openalex.org/C2776637919","wikidata":"https://www.wikidata.org/wiki/Q624380","display_name":"Descent (aeronautics)","level":2,"score":0.5955060720443726},{"id":"https://openalex.org/C10494615","wikidata":"https://www.wikidata.org/wiki/Q17086765","display_name":"Proximal Gradient Methods","level":4,"score":0.5842746496200562},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5576305389404297},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.5449283719062805},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.4796474575996399},{"id":"https://openalex.org/C206688291","wikidata":"https://www.wikidata.org/wiki/Q7617819","display_name":"Stochastic gradient descent","level":3,"score":0.4361156225204468},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.41793322563171387},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3853724002838135},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.37535402178764343},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.26157695055007935},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.15134993195533752},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.10531109571456909},{"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/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1090/mcom/4103","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/4103","pdf_url":null,"source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},{"id":"pmh:oai:ora.ox.ac.uk:uuid:91db83ba-c6a3-45b2-900d-e9985bda29d6","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306402636","display_name":"Oxford University Research Archive (ORA) (University of Oxford)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I40120149","host_organization_name":"University of Oxford","host_organization_lineage":["https://openalex.org/I40120149"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symplectic Elements","raw_type":"http://purl.org/coar/resource_type/c_dcae04bc"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W1460189015","https://openalex.org/W1832379062","https://openalex.org/W1984332158","https://openalex.org/W2166126709","https://openalex.org/W2525518963","https://openalex.org/W2897048230","https://openalex.org/W2901838001","https://openalex.org/W2928207644","https://openalex.org/W2962730199","https://openalex.org/W2963433607","https://openalex.org/W3014408215","https://openalex.org/W3057525668","https://openalex.org/W3100387237","https://openalex.org/W3208582873","https://openalex.org/W4236434641","https://openalex.org/W4402362980","https://openalex.org/W6600120041"],"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/W4224283687"],"abstract_inverted_index":{"We":[0],"study":[1],"gradient":[2],"descent":[3],"with":[4,122],"backtracking":[5],"line":[6],"search":[7],"(GD-BLS)":[8],"to":[9,116],"solve":[10],"the":[11,49],"noisy":[12],"optimization":[13],"problem":[14],"\u03b8":[15,24,32,54,61,85,88,118],"\u22c6":[16,89,119],"\u2254":[17,56],"a":[18],"r":[19],"g":[20],"m":[21],"i":[22],"n":[23],"\u2208":[25],"R":[26],"d":[27],"E":[28,57,81],"[":[29,58,82],"f":[30,59,86],"(":[31,53,60,87],",":[33,46,62,90,104],"Z":[34,63,91],")":[35,55,64,92],"]":[36,65,95],"\\theta":[37,120],"_\\star":[38,102,121],"\u2254argmin_{\\theta":[39],"\\in":[40],"\\mathbb":[41,43,98],"{R}^d}":[42],"{E}[f(\\theta":[44,68],",Z)]":[45,69],"imposing":[47],"that":[48,80,108],"objective":[50],"function":[51],"F":[52],"F(\\theta":[66],")\u2254\\mathbb":[67],"is":[70],"strictly":[71],"convex":[72],"but":[73],"not":[74],"necessarily":[75],"L":[76,77],"-smooth.":[78],"Assuming":[79],"\u2016":[83,93],"\u2207":[84],"2":[94],">":[96],"\u221e":[97],"{E}[\\|\\nabla":[99],"_\\theta":[100],"f(\\theta":[101],",Z)\\|^2]>\\infty":[103],"we":[105],"first":[106],"prove":[107],"sample":[109],"average":[110],"approximation":[111],"based":[112],"on":[113],"GD-BLS":[114],"allows":[115],"estimate":[117],"an":[123],"error":[124],"of":[125],"size":[126],"O":[127],"P":[128]},"counts_by_year":[],"updated_date":"2026-08-26T07:47:46.906454","created_date":"2025-10-10T00:00:00"}