{"id":"https://openalex.org/W7130653861","doi":"https://doi.org/10.1137/24m1697268","title":"Mirror Descent Algorithms with Nearly Dimension-Independent Rates for Differentially-Private Stochastic Saddle-Point Problems","display_name":"Mirror Descent Algorithms with Nearly Dimension-Independent Rates for Differentially-Private Stochastic Saddle-Point Problems","publication_year":2026,"publication_date":"2026-02-20","ids":{"openalex":"https://openalex.org/W7130653861","doi":"https://doi.org/10.1137/24m1697268"},"language":"en","primary_location":{"id":"doi:10.1137/24m1697268","is_oa":false,"landing_page_url":"https://doi.org/10.1137/24m1697268","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"is_oa":false,"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 Optimization","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/A5126451708","display_name":"Tom\u00e1s Gonz\u00e1lez","orcid":null},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Tom\u00e1s Gonz\u00e1lez","raw_affiliation_strings":["Machine Learning Department, Carnegie Mellon University, Pittsburgh, PA 15213 USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Machine Learning Department, Carnegie Mellon University, Pittsburgh, PA 15213 USA","institution_ids":["https://openalex.org/I74973139"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5126207489","display_name":"Crist\u00f3bal Guzm\u00e1n","orcid":null},"institutions":[{"id":"https://openalex.org/I162148367","display_name":"Pontificia Universidad Cat\u00f3lica de Chile","ror":"https://ror.org/04teye511","country_code":"CL","type":"education","lineage":["https://openalex.org/I162148367"]}],"countries":["CL"],"is_corresponding":false,"raw_author_name":"Crist\u00f3bal Guzm\u00e1n","raw_affiliation_strings":["Institute for Mathematical and Computational Engineering, Faculty of Mathematics and School of Engineering, Pontificia Universidad Cat\u00f3lica de Chile and Google Research, Regi\u00f3n Metropolitana, Chile"],"raw_orcid":"https://orcid.org/0000-0002-1498-2055","affiliations":[{"raw_affiliation_string":"Institute for Mathematical and Computational Engineering, Faculty of Mathematics and School of Engineering, Pontificia Universidad Cat\u00f3lica de Chile and Google Research, Regi\u00f3n Metropolitana, Chile","institution_ids":["https://openalex.org/I162148367"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5073457791","display_name":"Courtney Paquette","orcid":"https://orcid.org/0009-0005-5470-6249"},"institutions":[{"id":"https://openalex.org/I5023651","display_name":"McGill University","ror":"https://ror.org/01pxwe438","country_code":"CA","type":"education","lineage":["https://openalex.org/I5023651"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Courtney Paquette","raw_affiliation_strings":["Department of Mathematics and Statistics, McGill University and Google DeepMind, Quebec H3A 0G4, Canada"],"raw_orcid":"https://orcid.org/0009-0005-5470-6249","affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, McGill University and Google DeepMind, Quebec H3A 0G4, Canada","institution_ids":["https://openalex.org/I5023651"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.14918603,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"36","issue":"1","first_page":"233","last_page":"262"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.43779999017715454,"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":0.43779999017715454,"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/T11413","display_name":"Risk and Portfolio Optimization","score":0.23669999837875366,"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":0.0658000037074089,"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/stochastic-gradient-descent","display_name":"Stochastic gradient descent","score":0.4253000020980835},{"id":"https://openalex.org/keywords/descent","display_name":"Descent (aeronautics)","score":0.34869998693466187},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.33709999918937683},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.2930999994277954},{"id":"https://openalex.org/keywords/minification","display_name":"Minification","score":0.2883000075817108},{"id":"https://openalex.org/keywords/coordinate-descent","display_name":"Coordinate descent","score":0.28529998660087585},{"id":"https://openalex.org/keywords/approximation-algorithm","display_name":"Approximation algorithm","score":0.2849999964237213}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7459999918937683},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5504999756813049},{"id":"https://openalex.org/C206688291","wikidata":"https://www.wikidata.org/wiki/Q7617819","display_name":"Stochastic gradient descent","level":3,"score":0.4253000020980835},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3716999888420105},{"id":"https://openalex.org/C2776637919","wikidata":"https://www.wikidata.org/wiki/Q624380","display_name":"Descent (aeronautics)","level":2,"score":0.34869998693466187},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3458999991416931},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.33709999918937683},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2971000075340271},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.2930999994277954},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.2883000075817108},{"id":"https://openalex.org/C157553263","wikidata":"https://www.wikidata.org/wiki/Q5168004","display_name":"Coordinate descent","level":2,"score":0.28529998660087585},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.2849999964237213},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.2838999927043915},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.2824000120162964},{"id":"https://openalex.org/C194387892","wikidata":"https://www.wikidata.org/wiki/Q1747770","display_name":"Stochastic optimization","level":2,"score":0.28119999170303345},{"id":"https://openalex.org/C55479107","wikidata":"https://www.wikidata.org/wiki/Q97663916","display_name":"Stochastic approximation","level":3,"score":0.27489998936653137},{"id":"https://openalex.org/C2987595161","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Optimization algorithm","level":2,"score":0.2736999988555908},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.2558000087738037}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/24m1697268","is_oa":false,"landing_page_url":"https://doi.org/10.1137/24m1697268","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"is_oa":false,"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 Optimization","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5843948711","display_name":null,"funder_award_id":"1210362","funder_id":"https://openalex.org/F4320338073","funder_display_name":"Fondo Nacional de Desarrollo Cient\u00edfico y Tecnol\u00f3gico"}],"funders":[{"id":"https://openalex.org/F4320309327","display_name":"Google","ror":"https://ror.org/00njsd438"},{"id":"https://openalex.org/F4320313934","display_name":"Institut national de recherche en informatique et en automatique (INRIA)","ror":"https://ror.org/02kvxyf05"},{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"},{"id":"https://openalex.org/F4320334841","display_name":"Fonds de recherche du Qu\u00e9bec \u2013 Nature et technologies","ror":"https://ror.org/00b9f9778"},{"id":"https://openalex.org/F4320338073","display_name":"Fondo Nacional de Desarrollo Cient\u00edfico y Tecnol\u00f3gico","ror":"https://ror.org/02ap3w078"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W1487404723","https://openalex.org/W1983127118","https://openalex.org/W1985310469","https://openalex.org/W1992208280","https://openalex.org/W2000138211","https://openalex.org/W2021426916","https://openalex.org/W2035490465","https://openalex.org/W2059602082","https://openalex.org/W2127208184","https://openalex.org/W2166116275","https://openalex.org/W2213102012","https://openalex.org/W2507742300","https://openalex.org/W2963450292","https://openalex.org/W3147063886","https://openalex.org/W4205228770","https://openalex.org/W4237551148","https://openalex.org/W4247869890","https://openalex.org/W4415795237","https://openalex.org/W4415797397"],"related_works":[],"abstract_inverted_index":{"Abstract.":[0],"We":[1,17],"study":[2],"the":[3,12,35,71,74,80,91,113,142,151,186,202],"problem":[4,75],"of":[5,41,62,73,112,115,122,175,195,201,213],"differentially-private":[6],"(DP)":[7],"stochastic":[8,25,55,147,167],"(convex-concave)":[9],"saddle-points":[10],"in":[11,150],"[Formula:":[13,19,63,67,77,97,123,152,176,189],"see":[14,20,64,68,78,98,124,153,177,190],"text]":[15,69,79,99,125,154],"setting.":[16],"propose":[18],"text]-DP":[21],"algorithms":[22,58,170],"based":[23,159],"on":[24,160],"mirror":[26],"descent":[27],"that":[28,43,90,130,156],"attain":[29,59,171],"nearly":[30],"dimension-independent":[31],"convergence":[32],"rates":[33],"for":[34,48,145],"expected":[36],"duality":[37,92],"gap,":[38],"a":[39,60,119],"type":[40],"guarantee":[42],"was":[44],"known":[45],"before":[46],"only":[47],"bilinear":[49],"objectives.":[50],"For":[51,163],"convex-concave":[52],"and":[53,76,165,179],"first-order-smooth":[54,166],"objectives,":[56,168],"our":[57,116,132,169],"rate":[61,109,187],"text],":[65,178],"where":[66],"is":[70,94,157],"dimension":[72],"dataset":[81],"size.":[82],"Under":[83],"an":[84,172],"additional":[85],"second-order-smoothness":[86],"assumption,":[87],"we":[88,128,184],"show":[89,129],"gap":[93],"bounded":[95],"by":[96,103],"with":[100,134],"high":[101],"probability,":[102],"using":[104],"bias-reduced":[105],"gradient":[106],"estimators.":[107],"This":[108],"provides":[110],"evidence":[111],"near-optimality":[114],"approach,":[117],"since":[118],"lower":[120],"bound":[121],"exists.":[126],"Finally,":[127],"combining":[131],"methods":[133],"acceleration":[135],"techniques":[136],"from":[137],"online":[138],"learning":[139],"leads":[140],"to":[141,188,193],"first":[143],"algorithm":[144],"DP":[146],"convex":[148,164],"optimization":[149],"setting":[155],"not":[158],"Frank\u2013Wolfe":[161],"methods.":[162],"excess":[173],"risk":[174],"when":[180],"additionally":[181],"assuming":[182],"second-order-smoothness,":[183],"improve":[185],"text].":[191],"Instrumental":[192],"all":[194],"these":[196],"results":[197],"are":[198],"various":[199],"extensions":[200],"classical":[203],"Maurey":[204],"sparsification":[205],"lemma":[206],"[":[207],"34":[208],"],":[209],"which":[210],"may":[211],"be":[212],"independent":[214],"interest.":[215]},"counts_by_year":[],"updated_date":"2026-08-22T07:34:49.880490","created_date":"2026-02-20T00:00:00"}