{"id":"https://openalex.org/W7127406075","doi":"https://doi.org/10.48550/arxiv.2602.01339","title":"Finding Differentially Private Second Order Stationary Points in Stochastic Minimax Optimization","display_name":"Finding Differentially Private Second Order Stationary Points in Stochastic Minimax Optimization","publication_year":2026,"publication_date":"2026-02-01","ids":{"openalex":"https://openalex.org/W7127406075","doi":"https://doi.org/10.48550/arxiv.2602.01339"},"language":null,"primary_location":{"id":"pmh:doi:10.48550/arxiv.2602.01339","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":null,"any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5042101947","display_name":"Difei Xu","orcid":"https://orcid.org/0000-0002-4634-0639"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xu, Difei","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5124890860","display_name":"Youming Tao","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Tao, Youming","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5124923414","display_name":"Meng Ding","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ding, Meng","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5124962927","display_name":"Chenglin Fan","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Fan, Chenglin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5124900296","display_name":"Di Wang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wang, Di","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.8937000036239624,"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":0.8937000036239624,"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/T10764","display_name":"Privacy-Preserving Technologies in Data","score":0.054999999701976776,"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":0.017000000923871994,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/minimax","display_name":"Minimax","score":0.8348000049591064},{"id":"https://openalex.org/keywords/population","display_name":"Population","score":0.5378000140190125},{"id":"https://openalex.org/keywords/stationary-point","display_name":"Stationary point","score":0.5141000151634216},{"id":"https://openalex.org/keywords/variance","display_name":"Variance (accounting)","score":0.48649999499320984},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.459199994802475},{"id":"https://openalex.org/keywords/minification","display_name":"Minification","score":0.439300000667572},{"id":"https://openalex.org/keywords/empirical-risk-minimization","display_name":"Empirical risk minimization","score":0.43529999256134033},{"id":"https://openalex.org/keywords/matching","display_name":"Matching (statistics)","score":0.4018000066280365},{"id":"https://openalex.org/keywords/noise","display_name":"Noise (video)","score":0.39989998936653137}],"concepts":[{"id":"https://openalex.org/C149728462","wikidata":"https://www.wikidata.org/wiki/Q751319","display_name":"Minimax","level":2,"score":0.8348000049591064},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5824999809265137},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5454000234603882},{"id":"https://openalex.org/C2908647359","wikidata":"https://www.wikidata.org/wiki/Q2625603","display_name":"Population","level":2,"score":0.5378000140190125},{"id":"https://openalex.org/C189237950","wikidata":"https://www.wikidata.org/wiki/Q2500758","display_name":"Stationary point","level":2,"score":0.5141000151634216},{"id":"https://openalex.org/C196083921","wikidata":"https://www.wikidata.org/wiki/Q7915758","display_name":"Variance (accounting)","level":2,"score":0.48649999499320984},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.459199994802475},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.439300000667572},{"id":"https://openalex.org/C107321475","wikidata":"https://www.wikidata.org/wiki/Q5374254","display_name":"Empirical risk minimization","level":2,"score":0.43529999256134033},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.4018000066280365},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.39989998936653137},{"id":"https://openalex.org/C62644790","wikidata":"https://www.wikidata.org/wiki/Q3454689","display_name":"Variance reduction","level":3,"score":0.39430001378059387},{"id":"https://openalex.org/C4199805","wikidata":"https://www.wikidata.org/wiki/Q2725903","display_name":"Gaussian noise","level":2,"score":0.38839998841285706},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.36559998989105225},{"id":"https://openalex.org/C55479107","wikidata":"https://www.wikidata.org/wiki/Q97663916","display_name":"Stochastic approximation","level":3,"score":0.3596000075340271},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.35920000076293945},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.3382999897003174},{"id":"https://openalex.org/C194387892","wikidata":"https://www.wikidata.org/wiki/Q1747770","display_name":"Stochastic optimization","level":2,"score":0.33730000257492065},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3310999870300293},{"id":"https://openalex.org/C138777275","wikidata":"https://www.wikidata.org/wiki/Q6884054","display_name":"Mixing (physics)","level":2,"score":0.32420000433921814},{"id":"https://openalex.org/C127491075","wikidata":"https://www.wikidata.org/wiki/Q7617825","display_name":"Stochastic modelling","level":2,"score":0.3127000033855438},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.31049999594688416},{"id":"https://openalex.org/C61326573","wikidata":"https://www.wikidata.org/wiki/Q1496376","display_name":"Gaussian process","level":3,"score":0.2957000136375427},{"id":"https://openalex.org/C2985420695","wikidata":"https://www.wikidata.org/wiki/Q175199","display_name":"Population variance","level":3,"score":0.2752000093460083},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.27300000190734863},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.263700008392334},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.2623000144958496},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.2508000135421753}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:doi:10.48550/arxiv.2602.01339","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},{"id":"doi:10.48550/arxiv.2602.01339","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.01339","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:doi:10.48550/arxiv.2602.01339","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},"sustainable_development_goals":[{"score":0.47289329767227173,"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0],"provide":[1],"the":[2,6,46,95,106,155],"first":[3,47],"study":[4],"of":[5,8,54,97,114],"problem":[7],"finding":[9],"differentially":[10],"private":[11,160],"(DP)":[12],"second-order":[13,136],"stationary":[14,29,137],"points":[15,30],"(SOSP)":[16],"in":[17],"stochastic":[18,39,98],"(non-convex)":[19],"minimax":[20,32],"optimization.":[21],"Existing":[22],"literature":[23],"either":[24],"focuses":[25],"only":[26],"on":[27,35],"first-order":[28,65,161],"for":[31,37,45,132,143,151,159],"problems":[33],"or":[34],"SOSP":[36],"classical":[38],"minimization":[40],"problems.":[41],"This":[42],"work":[43],"provides,":[44],"time,":[48],"a":[49,63,69,89,111],"unified":[50,112],"and":[51,57,78,100,117,124,147],"detailed":[52],"treatment":[53,113],"both":[55,115],"empirical":[56,144],"population":[58,118,152],"risks.":[59],"Specifically,":[60],"we":[61,128],"propose":[62],"purely":[64],"method":[66],"that":[67,93],"combines":[68],"nested":[70],"gradient":[71],"descent--ascent":[72],"scheme":[73],"with":[74,139],"SPIDER-style":[75],"variance":[76,99],"reduction":[77],"Gaussian":[79],"perturbations":[80],"to":[81],"ensure":[82],"privacy.":[83],"A":[84],"key":[85],"technical":[86],"device":[87],"is":[88],"block-wise":[90],"($q$-period)":[91],"analysis":[92],"controls":[94],"accumulation":[96],"privacy":[101],"noise":[102],"without":[103],"summing":[104],"over":[105],"full":[107],"iteration":[108],"horizon,":[109],"yielding":[110],"empirical-risk":[116],"formulations.":[119],"Under":[120],"standard":[121],"smoothness,":[122],"Hessian-Lipschitzness,":[123],"strong":[125],"concavity":[126],"assumptions,":[127],"establish":[129],"high-probability":[130],"guarantees":[131],"reaching":[133],"an":[134],"$(\u03b1,\\sqrt{\u03c1_\u03a6\u03b1})$-approximate":[135],"point":[138],"$\u03b1=":[140],"\\mathcal{O}(":[141],"(\\frac{\\sqrt{d}}{n\\varepsilon})^{2/3})$":[142],"risk":[145],"objectives":[146],"$\\mathcal{O}(\\frac{1}{n^{1/3}}":[148],"+":[149],"(\\frac{\\sqrt{d}}{n\\varepsilon})^{1/2})$":[150],"objectives,":[153],"matching":[154],"best":[156],"known":[157],"rates":[158],"stationarity.":[162]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2026-02-04T00:00:00"}
