{"id":"https://openalex.org/W4286233277","doi":"https://doi.org/10.48550/arxiv.2207.08347","title":"Private Convex Optimization in General Norms","display_name":"Private Convex Optimization in General Norms","publication_year":2022,"publication_date":"2022-07-18","ids":{"openalex":"https://openalex.org/W4286233277","doi":"https://doi.org/10.48550/arxiv.2207.08347"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2207.08347","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2207.08347","pdf_url":"https://arxiv.org/pdf/2207.08347","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":"","raw_type":"text"},"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2207.08347","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5038687630","display_name":"Sivakanth Gopi","orcid":"https://orcid.org/0000-0001-9706-4171"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Gopi, Sivakanth","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5024980585","display_name":"Yin Tat Lee","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lee, Yin Tat","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5085627312","display_name":"Daogao Liu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Liu, Daogao","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5089489804","display_name":"Ruoqi Shen","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Shen, Ruoqi","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5101553599","display_name":"Kevin Tian","orcid":"https://orcid.org/0000-0002-9876-3991"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Tian, Kevin","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5038687630"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10764","display_name":"Privacy-Preserving Technologies in Data","score":0.9944000244140625,"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/T10764","display_name":"Privacy-Preserving Technologies in Data","score":0.9944000244140625,"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/T12229","display_name":"Pharmacological Effects and Toxicity Studies","score":0.983299970626831,"subfield":{"id":"https://openalex.org/subfields/2735","display_name":"Pediatrics, Perinatology and Child Health"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},{"id":"https://openalex.org/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9814000129699707,"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/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.73662930727005},{"id":"https://openalex.org/keywords/differential-privacy","display_name":"Differential privacy","score":0.5974636077880859},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.5888078212738037},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5754281878471375},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.5374845266342163},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5201214551925659},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.49712279438972473},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.4884871244430542},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.47820234298706055},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.4674433469772339},{"id":"https://openalex.org/keywords/empirical-risk-minimization","display_name":"Empirical risk minimization","score":0.4577966332435608},{"id":"https://openalex.org/keywords/convex-body","display_name":"Convex body","score":0.44539666175842285},{"id":"https://openalex.org/keywords/stochastic-gradient-descent","display_name":"Stochastic gradient descent","score":0.41153091192245483},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4081129729747772},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3524775207042694},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.26405876874923706},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.23299476504325867},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.18158653378486633},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.17863819003105164},{"id":"https://openalex.org/keywords/law","display_name":"Law","score":0.1085425317287445},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.09236574172973633},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08889627456665039}],"concepts":[{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.73662930727005},{"id":"https://openalex.org/C23130292","wikidata":"https://www.wikidata.org/wiki/Q5275358","display_name":"Differential privacy","level":2,"score":0.5974636077880859},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.5888078212738037},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5754281878471375},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.5374845266342163},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5201214551925659},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.49712279438972473},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.4884871244430542},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.47820234298706055},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.4674433469772339},{"id":"https://openalex.org/C107321475","wikidata":"https://www.wikidata.org/wiki/Q5374254","display_name":"Empirical risk minimization","level":2,"score":0.4577966332435608},{"id":"https://openalex.org/C134912446","wikidata":"https://www.wikidata.org/wiki/Q5166516","display_name":"Convex body","level":4,"score":0.44539666175842285},{"id":"https://openalex.org/C206688291","wikidata":"https://www.wikidata.org/wiki/Q7617819","display_name":"Stochastic gradient descent","level":3,"score":0.41153091192245483},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4081129729747772},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3524775207042694},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.26405876874923706},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.23299476504325867},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.18158653378486633},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.17863819003105164},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.1085425317287445},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.09236574172973633},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08889627456665039},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","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}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2207.08347","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2207.08347","pdf_url":"https://arxiv.org/pdf/2207.08347","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":"","raw_type":"text"},{"id":"doi:10.48550/arxiv.2207.08347","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2207.08347","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2207.08347","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2207.08347","pdf_url":"https://arxiv.org/pdf/2207.08347","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":"","raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4286233277.pdf","grobid_xml":"https://content.openalex.org/works/W4286233277.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2536155658","https://openalex.org/W2981981504","https://openalex.org/W4361791424","https://openalex.org/W3037866069","https://openalex.org/W4297796978","https://openalex.org/W3006853572","https://openalex.org/W4299587028","https://openalex.org/W2398277178","https://openalex.org/W3156389829","https://openalex.org/W3037299979"],"abstract_inverted_index":{"We":[0,67],"propose":[1],"a":[2,25,45,56,171],"new":[3],"framework":[4,96],"for":[5,128,134,147],"differentially":[6],"private":[7,103],"optimization":[8,105,130,180],"of":[9,59],"convex":[10,50,86,93,104],"functions":[11],"which":[12,29,47],"are":[13,22,182],"Lipschitz":[14,129],"in":[15,106,131],"an":[16],"arbitrary":[17],"norm":[18,176,179],"$\\|\\cdot\\|$.":[19],"Our":[20,95,174],"algorithms":[21],"based":[23],"on":[24],"regularized":[26],"exponential":[27],"mechanism":[28,71],"samples":[30],"from":[31,92],"the":[32,39,98,121,142,156],"density":[33],"$\\propto":[34],"\\exp(-k(F+\u03bcr))$":[35],"where":[36],"$F$":[37],"is":[38,44,48,97],"empirical":[40],"loss":[41],"and":[42,76,83,110,177],"$r$":[43],"regularizer":[46],"strongly":[49],"with":[51,184],"respect":[52],"to":[53,64,100,102],"$\\|\\cdot\\|$,":[54],"generalizing":[55],"recent":[57,157],"work":[58],"[Gopi,":[60],"Lee,":[61],"Liu":[62],"'22]":[63],"non-Euclidean":[65],"settings.":[66],"show":[68],"that":[69],"this":[70],"satisfies":[72],"Gaussian":[73],"differential":[74],"privacy":[75,122],"solves":[77],"both":[78],"DP-ERM":[79],"(empirical":[80],"risk":[81],"minimization)":[82],"DP-SCO":[84],"(stochastic":[85],"optimization)":[87],"by":[88,117,155,168],"using":[89],"localization":[90],"tools":[91],"geometry.":[94],"first":[99,143],"apply":[101],"general":[107],"normed":[108],"spaces":[109],"directly":[111],"recovers":[112],"non-private":[113],"SCO":[114],"rates":[115],"achieved":[116],"mirror":[118],"descent":[119],"as":[120],"parameter":[123],"$\u03b5\\to":[124],"\\infty$.":[125],"As":[126],"applications,":[127],"$\\ell_p$":[132,175],"norms":[133],"all":[135],"$p":[136,148],"\\in":[137],"(1,":[138],"2)$,":[139],"we":[140,151,190],"obtain":[141],"optimal":[144],"privacy-utility":[145],"tradeoffs;":[146],"=":[149],"1$,":[150],"improve":[152],"tradeoffs":[153],"obtained":[154],"works":[158],"[Asi,":[159],"Feldman,":[160],"Koren,":[161],"Talwar":[162],"'21,":[163],"Bassily,":[164],"Guzman,":[165],"Nandi":[166],"'21]":[167],"at":[169],"least":[170],"logarithmic":[172],"factor.":[173],"Schatten-$p$":[178],"frameworks":[181],"complemented":[183],"polynomial-time":[185],"samplers":[186],"whose":[187],"query":[188],"complexity":[189],"explicitly":[191],"bound.":[192]},"counts_by_year":[{"year":2024,"cited_by_count":2}],"updated_date":"2026-03-10T16:38:18.471706","created_date":"2025-10-10T00:00:00"}