{"id":"https://openalex.org/W3129962851","doi":"https://doi.org/10.1109/tac.2021.3059427","title":"Differentially Private Distributed Optimization via State and Direction Perturbation in Multiagent Systems","display_name":"Differentially Private Distributed Optimization via State and Direction Perturbation in Multiagent Systems","publication_year":2021,"publication_date":"2021-02-16","ids":{"openalex":"https://openalex.org/W3129962851","doi":"https://doi.org/10.1109/tac.2021.3059427","mag":"3129962851"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2021.3059427","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2021.3059427","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","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/A5082206880","display_name":"Tie Ding","orcid":"https://orcid.org/0000-0002-2169-8861"},"institutions":[{"id":"https://openalex.org/I1327237609","display_name":"Ministry of Education of the People's Republic of China","ror":"https://ror.org/01mv9t934","country_code":"CN","type":"funder","lineage":["https://openalex.org/I1327237609","https://openalex.org/I4210127390"]},{"id":"https://openalex.org/I183067930","display_name":"Shanghai Jiao Tong University","ror":"https://ror.org/0220qvk04","country_code":"CN","type":"education","lineage":["https://openalex.org/I183067930"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Tie Ding","raw_affiliation_strings":["Department of Automation, Shanghai Jiao Tong University, Shanghai, China","the Key Laboratory of System Control and Information Processing, Ministry of Education of China, Shanghai, China"],"affiliations":[{"raw_affiliation_string":"Department of Automation, Shanghai Jiao Tong University, Shanghai, China","institution_ids":["https://openalex.org/I183067930"]},{"raw_affiliation_string":"the Key Laboratory of System Control and Information Processing, Ministry of Education of China, Shanghai, China","institution_ids":["https://openalex.org/I1327237609"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5007013035","display_name":"Shanying Zhu","orcid":"https://orcid.org/0000-0003-4860-4519"},"institutions":[{"id":"https://openalex.org/I1327237609","display_name":"Ministry of Education of the People's Republic of China","ror":"https://ror.org/01mv9t934","country_code":"CN","type":"funder","lineage":["https://openalex.org/I1327237609","https://openalex.org/I4210127390"]},{"id":"https://openalex.org/I183067930","display_name":"Shanghai Jiao Tong University","ror":"https://ror.org/0220qvk04","country_code":"CN","type":"education","lineage":["https://openalex.org/I183067930"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shanying Zhu","raw_affiliation_strings":["Department of Automation, Shanghai Jiao Tong University, Shanghai, China","the Key Laboratory of System Control and Information Processing, Ministry of Education of China, Shanghai, China"],"affiliations":[{"raw_affiliation_string":"Department of Automation, Shanghai Jiao Tong University, Shanghai, China","institution_ids":["https://openalex.org/I183067930"]},{"raw_affiliation_string":"the Key Laboratory of System Control and Information Processing, Ministry of Education of China, Shanghai, China","institution_ids":["https://openalex.org/I1327237609"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5004668792","display_name":"Jianping He","orcid":"https://orcid.org/0000-0002-6253-7802"},"institutions":[{"id":"https://openalex.org/I1327237609","display_name":"Ministry of Education of the People's Republic of China","ror":"https://ror.org/01mv9t934","country_code":"CN","type":"funder","lineage":["https://openalex.org/I1327237609","https://openalex.org/I4210127390"]},{"id":"https://openalex.org/I183067930","display_name":"Shanghai Jiao Tong University","ror":"https://ror.org/0220qvk04","country_code":"CN","type":"education","lineage":["https://openalex.org/I183067930"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jianping He","raw_affiliation_strings":["Department of Automation, Shanghai Jiao Tong University, Shanghai, China","the Key Laboratory of System Control and Information Processing, Ministry of Education of China, Shanghai, China"],"affiliations":[{"raw_affiliation_string":"Department of Automation, Shanghai Jiao Tong University, Shanghai, China","institution_ids":["https://openalex.org/I183067930"]},{"raw_affiliation_string":"the Key Laboratory of System Control and Information Processing, Ministry of Education of China, Shanghai, China","institution_ids":["https://openalex.org/I1327237609"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5038267080","display_name":"Cailian Chen","orcid":"https://orcid.org/0000-0001-6533-8713"},"institutions":[{"id":"https://openalex.org/I183067930","display_name":"Shanghai Jiao Tong University","ror":"https://ror.org/0220qvk04","country_code":"CN","type":"education","lineage":["https://openalex.org/I183067930"]},{"id":"https://openalex.org/I1327237609","display_name":"Ministry of Education of the People's Republic of China","ror":"https://ror.org/01mv9t934","country_code":"CN","type":"funder","lineage":["https://openalex.org/I1327237609","https://openalex.org/I4210127390"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Cailian Chen","raw_affiliation_strings":["Department of Automation, Shanghai Jiao Tong University, Shanghai, China","the Key Laboratory of System Control and Information Processing, Ministry of Education of China, Shanghai, China"],"affiliations":[{"raw_affiliation_string":"Department of Automation, Shanghai Jiao Tong University, Shanghai, China","institution_ids":["https://openalex.org/I183067930"]},{"raw_affiliation_string":"the Key Laboratory of System Control and Information Processing, Ministry of Education of China, Shanghai, China","institution_ids":["https://openalex.org/I1327237609"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100690710","display_name":"Xinping Guan","orcid":"https://orcid.org/0009-0006-6233-8762"},"institutions":[{"id":"https://openalex.org/I183067930","display_name":"Shanghai Jiao Tong University","ror":"https://ror.org/0220qvk04","country_code":"CN","type":"education","lineage":["https://openalex.org/I183067930"]},{"id":"https://openalex.org/I1327237609","display_name":"Ministry of Education of the People's Republic of China","ror":"https://ror.org/01mv9t934","country_code":"CN","type":"funder","lineage":["https://openalex.org/I1327237609","https://openalex.org/I4210127390"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xinping Guan","raw_affiliation_strings":["Department of Automation, Shanghai Jiao Tong University, Shanghai, China","the Key Laboratory of System Control and Information Processing, Ministry of Education of China, Shanghai, China"],"affiliations":[{"raw_affiliation_string":"Department of Automation, Shanghai Jiao Tong University, Shanghai, China","institution_ids":["https://openalex.org/I183067930"]},{"raw_affiliation_string":"the Key Laboratory of System Control and Information Processing, Ministry of Education of China, Shanghai, China","institution_ids":["https://openalex.org/I1327237609"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5082206880"],"corresponding_institution_ids":["https://openalex.org/I1327237609","https://openalex.org/I183067930"],"apc_list":null,"apc_paid":null,"fwci":10.8306,"has_fulltext":false,"cited_by_count":104,"citation_normalized_percentile":{"value":0.98697321,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":100},"biblio":{"volume":"67","issue":"2","first_page":"722","last_page":"737"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10249","display_name":"Distributed Control Multi-Agent Systems","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T10249","display_name":"Distributed Control Multi-Agent Systems","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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":0.9976999759674072,"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/T10964","display_name":"Wireless Communication Security Techniques","score":0.9932000041007996,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/differential-privacy","display_name":"Differential privacy","score":0.8005917072296143},{"id":"https://openalex.org/keywords/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.7032544016838074},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6318922638893127},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5981680154800415},{"id":"https://openalex.org/keywords/perturbation","display_name":"Perturbation (astronomy)","score":0.5491155385971069},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5335795283317566},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.5093797445297241},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.5066242814064026},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.496298611164093},{"id":"https://openalex.org/keywords/distributed-algorithm","display_name":"Distributed algorithm","score":0.4539394974708557},{"id":"https://openalex.org/keywords/multi-agent-system","display_name":"Multi-agent system","score":0.4292910695075989},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3562381863594055},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.34241607785224915},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.29136016964912415},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.21234336495399475},{"id":"https://openalex.org/keywords/distributed-computing","display_name":"Distributed computing","score":0.13974934816360474},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.09264147281646729},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.06865906715393066}],"concepts":[{"id":"https://openalex.org/C23130292","wikidata":"https://www.wikidata.org/wiki/Q5275358","display_name":"Differential privacy","level":2,"score":0.8005917072296143},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.7032544016838074},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6318922638893127},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5981680154800415},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.5491155385971069},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5335795283317566},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.5093797445297241},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.5066242814064026},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.496298611164093},{"id":"https://openalex.org/C130120984","wikidata":"https://www.wikidata.org/wiki/Q2835898","display_name":"Distributed algorithm","level":2,"score":0.4539394974708557},{"id":"https://openalex.org/C41550386","wikidata":"https://www.wikidata.org/wiki/Q529909","display_name":"Multi-agent system","level":2,"score":0.4292910695075989},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3562381863594055},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.34241607785224915},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.29136016964912415},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.21234336495399475},{"id":"https://openalex.org/C120314980","wikidata":"https://www.wikidata.org/wiki/Q180634","display_name":"Distributed computing","level":1,"score":0.13974934816360474},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09264147281646729},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.06865906715393066},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tac.2021.3059427","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2021.3059427","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16","score":0.6200000047683716}],"awards":[{"id":"https://openalex.org/G1705705081","display_name":null,"funder_award_id":"61933009","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2943154064","display_name":null,"funder_award_id":"62003302","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G433333953","display_name":null,"funder_award_id":"61922058","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4996318773","display_name":null,"funder_award_id":"19XD1421800","funder_id":"https://openalex.org/F4320335796","funder_display_name":"Program of Shanghai Academic Research Leader"},{"id":"https://openalex.org/G5605764086","display_name":null,"funder_award_id":"62025305","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320335796","display_name":"Program of Shanghai Academic Research Leader","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W1159423507","https://openalex.org/W1494823099","https://openalex.org/W1571416372","https://openalex.org/W1920382817","https://openalex.org/W2020101172","https://openalex.org/W2022948311","https://openalex.org/W2044212084","https://openalex.org/W2092845654","https://openalex.org/W2096219879","https://openalex.org/W2103630167","https://openalex.org/W2174932653","https://openalex.org/W2291434103","https://openalex.org/W2313103852","https://openalex.org/W2341190528","https://openalex.org/W2343466252","https://openalex.org/W2344176906","https://openalex.org/W2406813000","https://openalex.org/W2509467699","https://openalex.org/W2527559122","https://openalex.org/W2568929096","https://openalex.org/W2605026797","https://openalex.org/W2613901841","https://openalex.org/W2737743075","https://openalex.org/W2763533254","https://openalex.org/W2790589536","https://openalex.org/W2799947113","https://openalex.org/W2802328008","https://openalex.org/W2894767817","https://openalex.org/W2911978475","https://openalex.org/W2914113355","https://openalex.org/W2962678892","https://openalex.org/W2963649943","https://openalex.org/W3098954913","https://openalex.org/W3100513551"],"related_works":["https://openalex.org/W3038283795","https://openalex.org/W2604501336","https://openalex.org/W2734500670","https://openalex.org/W2558166297","https://openalex.org/W2315671126","https://openalex.org/W798507144","https://openalex.org/W2964481303","https://openalex.org/W3185235544","https://openalex.org/W1751413323","https://openalex.org/W4297791327"],"abstract_inverted_index":{"This":[0],"article":[1],"studies":[2],"the":[3,17,29,51,104,143,158,173,183,188,207],"problem":[4,204],"of":[5,19,31,53,103,145,160,164,166],"distributed":[6,65,76],"optimization":[7,66],"in":[8,63,121,137],"multiagent":[9],"systems":[10],"where":[11],"each":[12,33],"agent":[13,34],"seeks":[14],"to":[15,36,111,205],"minimize":[16],"sum":[18,144],"all":[20,146],"agents\u2019":[21],"objective":[22,39],"functions":[23,148],"using":[24],"only":[25,140],"local":[26],"information.":[27],"Under":[28],"requirement":[30],"security,":[32],"needs":[35],"keep":[37],"its":[38],"function":[40],"private":[41],"from":[42,101],"other":[43],"agents":[44],"and":[45,56,82,94,123,186,193],"potential":[46],"eavesdroppers.":[47],"We":[48],"first":[49],"prove":[50,134],"impossibility":[52],"guaranteeing":[54],"convergence":[55,136,154,175,194],"differential":[57,88,191],"privacy":[58,89,184,192],"simultaneously":[59],"by":[60,69,90,139],"perturbing":[61,91],"states":[62,93],"exact":[64],"algorithms.":[67],"Motivated":[68],"this":[70],"result,":[71],"we":[72,114,133,181],"design":[73],"a":[74,128,200],"completely":[75],"algorithm,":[77],"Distributed":[78],"algorithm":[79,119],"via":[80],"Direction":[81],"State":[83],"Perturbation":[84],"(DiaDSP),":[85],"that":[86,107,116,142,165],"achieves":[87],"both":[92],"directions":[95],"with":[96,127],"decaying":[97,109],"Laplace":[98],"noise.":[99],"Different":[100],"most":[102],"existing":[105],"works":[106],"require":[108],"stepsizes":[110],"ensure":[112],"convergence,":[113],"show":[115],"our":[117],"DiaDSP":[118],"converges":[120],"mean":[122,138],"almost":[124],"surely":[125],"even":[126],"constant":[129],"stepsize.":[130],"In":[131],"particular,":[132],"linear":[135],"assuming":[141],"cost":[147],"is":[149,155,177],"strongly":[150],"convex.":[151],"The":[152,169],"R-linear":[153],"proved":[156],"under":[157],"assumption":[159],"Lipschitz":[161],"gradients":[162],"instead":[163],"bounded":[167],"gradients.":[168],"optimal":[170],"stepsize":[171],"for":[172],"fastest":[174],"rate":[176],"also":[178],"established.":[179],"Moreover,":[180],"describe":[182],"properties":[185],"characterize":[187],"tradeoff":[189],"between":[190],"accuracy.":[195],"Simulations":[196],"are":[197],"conducted":[198],"on":[199],"typical":[201],"sensor":[202],"fusion":[203],"validate":[206],"theoretical":[208],"results.":[209]},"counts_by_year":[{"year":2026,"cited_by_count":5},{"year":2025,"cited_by_count":31},{"year":2024,"cited_by_count":33},{"year":2023,"cited_by_count":19},{"year":2022,"cited_by_count":10},{"year":2021,"cited_by_count":6}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}