{"id":"https://openalex.org/W4403308611","doi":"https://doi.org/10.1137/22m1536558","title":"High Probability Bounds for Stochastic Subgradient Schemes with Heavy Tailed Noise]","display_name":"High Probability Bounds for Stochastic Subgradient Schemes with Heavy Tailed Noise]","publication_year":2024,"publication_date":"2024-10-10","ids":{"openalex":"https://openalex.org/W4403308611","doi":"https://doi.org/10.1137/22m1536558"},"language":"en","primary_location":{"id":"doi:10.1137/22m1536558","is_oa":true,"landing_page_url":"https://doi.org/10.1137/22m1536558","pdf_url":null,"source":{"id":"https://openalex.org/S4210229561","display_name":"SIAM Journal on Mathematics of Data Science","issn_l":"2577-0187","issn":["2577-0187"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Mathematics of Data Science","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://doi.org/10.1137/22m1536558","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5064748172","display_name":"Daniela A. Parletta","orcid":null},"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":true,"raw_author_name":"Daniela Angela Parletta","raw_affiliation_strings":["CSML at Istituto Italiano di Tecnologia, 16163 Genova, Italy, and Department of Mathematics at University of Genoa, 16146 Genoa, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CSML at Istituto Italiano di Tecnologia, 16163 Genova, Italy, and Department of Mathematics at University of Genoa, 16146 Genoa, Italy","institution_ids":["https://openalex.org/I30771326"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5031096722","display_name":"Andrea Paudice","orcid":"https://orcid.org/0000-0003-1098-662X"},"institutions":[{"id":"https://openalex.org/I189158943","display_name":"University of Milan","ror":"https://ror.org/00wjc7c48","country_code":"IT","type":"education","lineage":["https://openalex.org/I189158943"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Andrea Paudice","raw_affiliation_strings":["Department of Computer Science at University of Milan, 20122 Milan, Italy"],"raw_orcid":"https://orcid.org/0000-0003-1098-662X","affiliations":[{"raw_affiliation_string":"Department of Computer Science at University of Milan, 20122 Milan, Italy","institution_ids":["https://openalex.org/I189158943"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5034260726","display_name":"Massimiliano Pontil","orcid":"https://orcid.org/0000-0001-9415-098X"},"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"]},{"id":"https://openalex.org/I45129253","display_name":"University College London","ror":"https://ror.org/02jx3x895","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I45129253"]}],"countries":["GB","IT"],"is_corresponding":false,"raw_author_name":"Massimiliano Pontil","raw_affiliation_strings":["CSML at Istituto Italiano di Tecnologia, 16163 Genova, Italy, and Department of Computer Science at UCL, London NW1 2AE, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CSML at Istituto Italiano di Tecnologia, 16163 Genova, Italy, and Department of Computer Science at UCL, London NW1 2AE, UK","institution_ids":["https://openalex.org/I45129253","https://openalex.org/I30771326"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5017463552","display_name":"Saverio Salzo","orcid":"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"]},{"id":"https://openalex.org/I861853513","display_name":"Sapienza University of Rome","ror":"https://ror.org/02be6w209","country_code":"IT","type":"education","lineage":["https://openalex.org/I861853513"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Saverio Salzo","raw_affiliation_strings":["CSML at Istituto Italiano di Tecnologia, 16163 Genova, Italy, and DIAG at Sapienza University of Rome, 00185 Rome, Italy"],"raw_orcid":"https://orcid.org/0000-0003-0494-9101","affiliations":[{"raw_affiliation_string":"CSML at Istituto Italiano di Tecnologia, 16163 Genova, Italy, and DIAG at Sapienza University of Rome, 00185 Rome, Italy","institution_ids":["https://openalex.org/I30771326","https://openalex.org/I861853513"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5064748172"],"corresponding_institution_ids":["https://openalex.org/I30771326"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.20963125,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"6","issue":"4","first_page":"953","last_page":"977"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11413","display_name":"Risk and Portfolio Optimization","score":0.9950000047683716,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T11413","display_name":"Risk and Portfolio Optimization","score":0.9950000047683716,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11720","display_name":"Probability and Risk Models","score":0.9945999979972839,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.987500011920929,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/subgradient-method","display_name":"Subgradient method","score":0.6221427917480469},{"id":"https://openalex.org/keywords/noise","display_name":"Noise (video)","score":0.4875034987926483},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.42272526025772095},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.41450417041778564},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3538314700126648},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.34491628408432007},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.337501585483551},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.15551644563674927},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.13850969076156616}],"concepts":[{"id":"https://openalex.org/C158968445","wikidata":"https://www.wikidata.org/wiki/Q7631150","display_name":"Subgradient method","level":2,"score":0.6221427917480469},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.4875034987926483},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.42272526025772095},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.41450417041778564},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3538314700126648},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.34491628408432007},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.337501585483551},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.15551644563674927},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.13850969076156616},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/22m1536558","is_oa":true,"landing_page_url":"https://doi.org/10.1137/22m1536558","pdf_url":null,"source":{"id":"https://openalex.org/S4210229561","display_name":"SIAM Journal on Mathematics of Data Science","issn_l":"2577-0187","issn":["2577-0187"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Mathematics of Data Science","raw_type":"journal-article"},{"id":"pmh:oai:iris.uniroma1.it:11573/1722248","is_oa":false,"landing_page_url":"https://hdl.handle.net/11573/1722248","pdf_url":null,"source":{"id":"https://openalex.org/S4377196107","display_name":"IRIS Research product catalog (Sapienza University of Rome)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.1137/22m1536558","is_oa":true,"landing_page_url":"https://doi.org/10.1137/22m1536558","pdf_url":null,"source":{"id":"https://openalex.org/S4210229561","display_name":"SIAM Journal on Mathematics of Data Science","issn_l":"2577-0187","issn":["2577-0187"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Mathematics of Data Science","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W2012501405","https://openalex.org/W2083459869","https://openalex.org/W2118369604","https://openalex.org/W2127332912","https://openalex.org/W2168909589","https://openalex.org/W2964198904","https://openalex.org/W2972939971","https://openalex.org/W3025638325","https://openalex.org/W4211092921","https://openalex.org/W4244633107","https://openalex.org/W4301435544"],"related_works":["https://openalex.org/W2095293854","https://openalex.org/W2363143319","https://openalex.org/W2757616806","https://openalex.org/W1984909291","https://openalex.org/W2127198104","https://openalex.org/W4243844638","https://openalex.org/W2117722264","https://openalex.org/W1964718673","https://openalex.org/W2331887418","https://openalex.org/W2129541103"],"abstract_inverted_index":{"In":[0,18],"this":[1,19,72],"work":[2],"we":[3],"study":[4],"high-probability":[5,46],"bounds":[6,83],"for":[7,36,84,113],"stochastic":[8,56],"subgradient":[9,43,57,60],"methods":[10,44,104],"under":[11],"heavy":[12],"tailed":[13],"noise":[14,22],"in":[15],"Hilbert":[16],"spaces.":[17],"setting":[20],"the":[21,54,89,100,124,127],"is":[23,39],"only":[24],"assumed":[25],"to":[26,32,77,99,122],"have":[27,66],"finite":[28,81],"variance":[29],"as":[30],"opposed":[31],"a":[33,50],"sub-Gaussian":[34],"distribution":[35],"which":[37,105],"it":[38],"known":[40],"that":[41,71],"standard":[42],"enjoy":[45],"bounds.":[47],"We":[48,69,91],"analyzed":[49],"clipped":[51],"version":[52],"of":[53,88,96,102,126],"projected":[55],"method,":[58],"where":[59],"estimates":[61],"are":[62,120],"truncated":[63],"whenever":[64],"they":[65],"large":[67],"norms.":[68],"show":[70,93],"clipping":[73],"strategy":[74],"leads":[75],"both":[76],"optimal":[78],"anytime":[79],"and":[80,109],"horizon":[82],"general":[85],"averaging":[86],"schemes":[87],"iterates.":[90],"also":[92],"an":[94,107],"application":[95],"our":[97],"proposal":[98],"case":[101],"kernel":[103],"gives":[106],"efficient":[108],"fully":[110],"implementable":[111],"algorithm":[112],"statistical":[114],"supervised":[115],"learning":[116],"problems.":[117],"Preliminary":[118],"experiments":[119],"shown":[121],"support":[123],"validity":[125],"method.":[128]},"counts_by_year":[],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}
