{"id":"https://openalex.org/W4415330520","doi":"https://doi.org/10.48550/arxiv.2507.23512","title":"Differentially Private Clipped-SGD: High-Probability Convergence with Arbitrary Clipping Level","display_name":"Differentially Private Clipped-SGD: High-Probability Convergence with Arbitrary Clipping Level","publication_year":2025,"publication_date":"2025-07-31","ids":{"openalex":"https://openalex.org/W4415330520","doi":"https://doi.org/10.48550/arxiv.2507.23512"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2507.23512","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2507.23512","pdf_url":"https://arxiv.org/pdf/2507.23512","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2507.23512","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5120055954","display_name":"Saleh Vatan Khah","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Khah, Saleh Vatan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5025224792","display_name":"Savelii Chezhegov","orcid":"https://orcid.org/0009-0003-7378-3210","observed_orcids":["https://orcid.org/0009-0003-7378-3210"]},"institutions":[{"id":"https://openalex.org/I67009956","display_name":"Iran University of Science and Technology","ror":"https://ror.org/01jw2p796","country_code":"IR","type":"education","lineage":["https://openalex.org/I67009956"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Chezhegov, Savelii","raw_affiliation_strings":["IUST"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"IUST","institution_ids":["https://openalex.org/I67009956"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Farahmand, Shahrokh","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I67009956","display_name":"Iran University of Science and Technology","ror":"https://ror.org/01jw2p796","country_code":"IR","type":"education","lineage":["https://openalex.org/I67009956"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Farahmand, Shahrokh","raw_affiliation_strings":["IUST"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"IUST","institution_ids":["https://openalex.org/I67009956"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5041080860","display_name":"Samuel Horv\u00e1th","orcid":"https://orcid.org/0000-0003-0619-9260","observed_orcids":["https://orcid.org/0000-0003-0619-9260"]},"institutions":[{"id":"https://openalex.org/I67009956","display_name":"Iran University of Science and Technology","ror":"https://ror.org/01jw2p796","country_code":"IR","type":"education","lineage":["https://openalex.org/I67009956"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Horv\u00e1th, Samuel","raw_affiliation_strings":["IUST"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"IUST","institution_ids":["https://openalex.org/I67009956"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5087594198","display_name":"Eduard Gorbunov","orcid":"https://orcid.org/0000-0002-3370-4130","observed_orcids":["https://orcid.org/0000-0002-3370-4130"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Gorbunov, Eduard","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":1,"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":0.6596999764442444,"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":0.6596999764442444,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.33570000529289246,"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/T12535","display_name":"Machine Learning and Data Classification","score":0.00019999999494757503,"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/differential-privacy","display_name":"differential privacy","score":0.8880000114440918},{"id":"https://openalex.org/keywords/gradient-clipping","display_name":"gradient clipping","score":0.9190000295639038},{"id":"https://openalex.org/keywords/heavy-tailed-noise","display_name":"heavy-tailed noise","score":0.9729999899864197},{"id":"https://openalex.org/keywords/nonconvex-optimization","display_name":"non-convex optimization","score":0.8429999947547913},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"convex optimization","score":0.7519999742507935},{"id":"https://openalex.org/keywords/gaussian-mechanism","display_name":"Gaussian mechanism","score":0.7009999752044678},{"id":"https://openalex.org/keywords/large-language-model-training","display_name":"large language model training","score":0.8119999766349792}],"concepts":[{"id":"https://openalex.org/C2776848632","wikidata":"https://www.wikidata.org/wiki/Q853463","display_name":"Clipping (morphology)","level":2,"score":0.7674000263214111},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.7109000086784363},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5187000036239624},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5040000081062317},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4684000015258789},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.4307999908924103},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.42149999737739563},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.3977000117301941},{"id":"https://openalex.org/C23130292","wikidata":"https://www.wikidata.org/wiki/Q5275358","display_name":"Differential privacy","level":2,"score":0.3930000066757202},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3885999917984009},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.3865000009536743},{"id":"https://openalex.org/C4199805","wikidata":"https://www.wikidata.org/wiki/Q2725903","display_name":"Gaussian noise","level":2,"score":0.36739999055862427},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3625999987125397},{"id":"https://openalex.org/C206688291","wikidata":"https://www.wikidata.org/wiki/Q7617819","display_name":"Stochastic gradient descent","level":3,"score":0.3537999987602234},{"id":"https://openalex.org/C179254644","wikidata":"https://www.wikidata.org/wiki/Q13222844","display_name":"Moment (physics)","level":2,"score":0.34139999747276306},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.2897999882698059},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.28760001063346863},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.2824999988079071},{"id":"https://openalex.org/C29265498","wikidata":"https://www.wikidata.org/wiki/Q7047719","display_name":"Noise measurement","level":3,"score":0.2782000005245209},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.2696000039577484},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.2667999863624573},{"id":"https://openalex.org/C5871375","wikidata":"https://www.wikidata.org/wiki/Q1780715","display_name":"Compact convergence","level":4,"score":0.2556000053882599},{"id":"https://openalex.org/C168167062","wikidata":"https://www.wikidata.org/wiki/Q1117970","display_name":"Component (thermodynamics)","level":2,"score":0.2542000114917755}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2507.23512","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2507.23512","pdf_url":"https://arxiv.org/pdf/2507.23512","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2507.23512","doi":"https://doi.org/10.48550/arxiv.2507.23512","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2507.23512","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2507.23512","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2507.23512","pdf_url":"https://arxiv.org/pdf/2507.23512","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4415330520.pdf","grobid_xml":"https://content.openalex.org/works/W4415330520.grobid-xml"},"referenced_works_count":13,"referenced_works":["https://openalex.org/W1575259140","https://openalex.org/W1594567720","https://openalex.org/W2341162003","https://openalex.org/W2964121744","https://openalex.org/W2971899460","https://openalex.org/W2990730264","https://openalex.org/W3046141244","https://openalex.org/W4388093081","https://openalex.org/W4399510488","https://openalex.org/W4403580163","https://openalex.org/W4407719475","https://openalex.org/W4415035193","https://openalex.org/W7125851080"],"related_works":["https://openalex.org/W4388032385","https://openalex.org/W3037261120","https://openalex.org/W4385080317","https://openalex.org/W7133245518","https://openalex.org/W4399151258","https://openalex.org/W3170173825","https://openalex.org/W4405955296","https://openalex.org/W3035493137","https://openalex.org/W4389073400","https://openalex.org/W4283705803"],"abstract_inverted_index":{"Gradient":[0],"clipping":[1,52,92,122],"is":[2,26,34,63],"a":[3,36,90,107,120,128,135,154],"fundamental":[4],"tool":[5],"in":[6,28],"Deep":[7],"Learning,":[8],"improving":[9],"the":[10,51,57,70,82,124,131,139,148],"high-probability":[11,46,84],"convergence":[12,47,85,158],"of":[13,39,59,130],"stochastic":[14],"first-order":[15],"methods":[16],"like":[17,69],"SGD,":[18],"AdaGrad,":[19],"and":[20,98,160],"Adam":[21],"under":[22,102],"heavy-tailed":[23,103],"noise,":[24,104],"which":[25,62],"common":[27],"training":[29],"large":[30],"language":[31],"models.":[32],"It":[33],"also":[35],"crucial":[37],"component":[38],"Differential":[40],"Privacy":[41],"(DP)":[42],"mechanisms.":[43],"However,":[44],"existing":[45,140],"analyses":[48],"typically":[49],"require":[50],"threshold":[53],"to":[54,95,127],"increase":[55],"with":[56,65,89,119,134],"number":[58],"optimization":[60,101],"steps,":[61],"incompatible":[64],"standard":[66],"DP":[67],"mechanisms":[68],"Gaussian":[71],"mechanism.":[72],"In":[73],"this":[74,78],"work,":[75],"we":[76],"close":[77],"gap":[79],"by":[80,106,151],"providing":[81,153],"first":[83],"analysis":[86],"for":[87],"DP-Clipped-SGD":[88],"fixed":[91,121],"level,":[93,123],"applicable":[94],"both":[96],"convex":[97],"non-convex":[99],"smooth":[100],"characterized":[105],"bounded":[108],"central":[109],"$\u03b1$-th":[110],"moment":[111],"assumption,":[112],"$\u03b1\\in":[113],"(1,2]$.":[114],"Our":[115],"results":[116],"show":[117],"that,":[118],"method":[125],"converges":[126],"neighborhood":[129,143],"optimal":[132],"solution":[133],"faster":[136],"rate":[137],"than":[138],"ones.":[141],"The":[142],"can":[144],"be":[145],"balanced":[146],"against":[147],"noise":[149],"introduced":[150],"DP,":[152],"refined":[155],"trade-off":[156],"between":[157],"speed":[159],"privacy":[161],"guarantees.":[162]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2025-10-19T00:00:00"}
