{"id":"https://openalex.org/W4395056611","doi":"https://doi.org/10.1109/tsp.2024.3392361","title":"Online Optimization Under Randomly Corrupted Attacks","display_name":"Online Optimization Under Randomly Corrupted Attacks","publication_year":2024,"publication_date":"2024-01-01","ids":{"openalex":"https://openalex.org/W4395056611","doi":"https://doi.org/10.1109/tsp.2024.3392361"},"language":"en","primary_location":{"id":"doi:10.1109/tsp.2024.3392361","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2024.3392361","pdf_url":null,"source":{"id":"https://openalex.org/S168680287","display_name":"IEEE Transactions on Signal Processing","issn_l":"1053-587X","issn":["1053-587X","1941-0476"],"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 Signal Processing","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/A5020083667","display_name":"Zhihai Qu","orcid":"https://orcid.org/0000-0003-4996-4583"},"institutions":[{"id":"https://openalex.org/I116953780","display_name":"Tongji University","ror":"https://ror.org/03rc6as71","country_code":"CN","type":"education","lineage":["https://openalex.org/I116953780"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Zhihai Qu","raw_affiliation_strings":["Department of Control Science and Engineering, College of Electronics and Information Engineering, Shanghai Research Institute for Intelligent Autonomous Systems, and Shanghai Institute of Intelligent Science and Technology, Tongji University, Shanghai, China"],"affiliations":[{"raw_affiliation_string":"Department of Control Science and Engineering, College of Electronics and Information Engineering, Shanghai Research Institute for Intelligent Autonomous Systems, and Shanghai Institute of Intelligent Science and Technology, Tongji University, Shanghai, China","institution_ids":["https://openalex.org/I116953780"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5037854048","display_name":"Xiuxian Li","orcid":"https://orcid.org/0000-0002-4938-0468"},"institutions":[{"id":"https://openalex.org/I116953780","display_name":"Tongji University","ror":"https://ror.org/03rc6as71","country_code":"CN","type":"education","lineage":["https://openalex.org/I116953780"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiuxian Li","raw_affiliation_strings":["Department of Control Science and Engineering, College of Electronics and Information Engineering, Shanghai Research Institute for Intelligent Autonomous Systems, and Shanghai Institute of Intelligent Science and Technology, Tongji University, Shanghai, China"],"affiliations":[{"raw_affiliation_string":"Department of Control Science and Engineering, College of Electronics and Information Engineering, Shanghai Research Institute for Intelligent Autonomous Systems, and Shanghai Institute of Intelligent Science and Technology, Tongji University, Shanghai, China","institution_ids":["https://openalex.org/I116953780"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100360961","display_name":"Li Li","orcid":"https://orcid.org/0000-0001-5097-9972"},"institutions":[{"id":"https://openalex.org/I116953780","display_name":"Tongji University","ror":"https://ror.org/03rc6as71","country_code":"CN","type":"education","lineage":["https://openalex.org/I116953780"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Li Li","raw_affiliation_strings":["Department of Control Science and Engineering, College of Electronics and Information Engineering, Shanghai Research Institute for Intelligent Autonomous Systems, and Shanghai Institute of Intelligent Science and Technology, Tongji University, Shanghai, China"],"affiliations":[{"raw_affiliation_string":"Department of Control Science and Engineering, College of Electronics and Information Engineering, Shanghai Research Institute for Intelligent Autonomous Systems, and Shanghai Institute of Intelligent Science and Technology, Tongji University, Shanghai, China","institution_ids":["https://openalex.org/I116953780"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5016417704","display_name":"Xinlei Yi","orcid":"https://orcid.org/0000-0003-4299-0471"},"institutions":[{"id":"https://openalex.org/I4210143601","display_name":"Decision Systems (United States)","ror":"https://ror.org/0434dpa13","country_code":"US","type":"company","lineage":["https://openalex.org/I4210143601"]},{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Xinlei Yi","raw_affiliation_strings":["Lab for Information &#x0026; Decision Systems, Massachusetts Institute of Technology, Cambridge, MA, USA"],"affiliations":[{"raw_affiliation_string":"Lab for Information &#x0026; Decision Systems, Massachusetts Institute of Technology, Cambridge, MA, USA","institution_ids":["https://openalex.org/I4210143601","https://openalex.org/I63966007"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5020083667"],"corresponding_institution_ids":["https://openalex.org/I116953780"],"apc_list":null,"apc_paid":null,"fwci":0.516,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.64753791,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"72","issue":null,"first_page":"2160","last_page":"2172"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12101","display_name":"Advanced Bandit Algorithms Research","score":0.9995999932289124,"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"}},"topics":[{"id":"https://openalex.org/T12101","display_name":"Advanced Bandit Algorithms Research","score":0.9995999932289124,"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/T12072","display_name":"Machine Learning and Algorithms","score":0.9955999851226807,"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/T12288","display_name":"Optimization and Search Problems","score":0.9939000010490417,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6024990677833557},{"id":"https://openalex.org/keywords/signal-processing","display_name":"Signal processing","score":0.418375700712204},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.38474351167678833},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.25979211926460266},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.1649511754512787},{"id":"https://openalex.org/keywords/radar","display_name":"Radar","score":0.12750890851020813}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6024990677833557},{"id":"https://openalex.org/C104267543","wikidata":"https://www.wikidata.org/wiki/Q208163","display_name":"Signal processing","level":3,"score":0.418375700712204},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.38474351167678833},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.25979211926460266},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.1649511754512787},{"id":"https://openalex.org/C554190296","wikidata":"https://www.wikidata.org/wiki/Q47528","display_name":"Radar","level":2,"score":0.12750890851020813}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tsp.2024.3392361","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2024.3392361","pdf_url":null,"source":{"id":"https://openalex.org/S168680287","display_name":"IEEE Transactions on Signal Processing","issn_l":"1053-587X","issn":["1053-587X","1941-0476"],"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 Signal Processing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4631057906","display_name":null,"funder_award_id":"62003243","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"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":43,"referenced_works":["https://openalex.org/W2068728923","https://openalex.org/W2513180554","https://openalex.org/W2888960341","https://openalex.org/W2951777528","https://openalex.org/W2964309292","https://openalex.org/W2998882145","https://openalex.org/W3122799214","https://openalex.org/W3123661679","https://openalex.org/W3174068174","https://openalex.org/W3183591154","https://openalex.org/W4297775537","https://openalex.org/W4319996469","https://openalex.org/W4389610366","https://openalex.org/W4391944659","https://openalex.org/W6602391300","https://openalex.org/W6640425456","https://openalex.org/W6677209015","https://openalex.org/W6681723013","https://openalex.org/W6681812773","https://openalex.org/W6686900281","https://openalex.org/W6713207811","https://openalex.org/W6725964698","https://openalex.org/W6737664043","https://openalex.org/W6743821447","https://openalex.org/W6748805329","https://openalex.org/W6750163886","https://openalex.org/W6754148645","https://openalex.org/W6755145423","https://openalex.org/W6755432591","https://openalex.org/W6758201434","https://openalex.org/W6760825779","https://openalex.org/W6762462524","https://openalex.org/W6768324076","https://openalex.org/W6779982451","https://openalex.org/W6788768515","https://openalex.org/W6802682914","https://openalex.org/W6810209262","https://openalex.org/W6810459761","https://openalex.org/W6811507423","https://openalex.org/W6839121823","https://openalex.org/W6847733083","https://openalex.org/W6849405947","https://openalex.org/W6850098910"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W2390279801","https://openalex.org/W4391913857","https://openalex.org/W2358668433","https://openalex.org/W4396701345","https://openalex.org/W2376932109","https://openalex.org/W2001405890","https://openalex.org/W4396696052"],"abstract_inverted_index":{"Existing":[0],"algorithms":[1,120],"in":[2,28,121,142],"online":[3,29,143],"optimization":[4],"usually":[5],"rely":[6],"on":[7,147],"trustful":[8],"information,":[9],"e.g.,":[10],"reliable":[11],"knowledge":[12],"of":[13,36,124,161],"gradients,":[14],"which":[15,40],"makes":[16],"them":[17],"vulnerable":[18],"to":[19,69,118,137],"attacks.":[20,127],"To":[21,46,128],"take":[22],"into":[23],"account":[24],"the":[25,34,48,65,105,110,122,135,159],"security":[26],"issue":[27],"optimization,":[30],"this":[31,132],"paper":[32,133],"investigates":[33],"effect":[35],"randomly":[37,49,125,139],"corrupted":[38,50,126,140],"attacks,":[39],"can":[41],"corrupt":[42],"gradient":[43],"information":[44],"arbitrarily.":[45],"conquer":[47],"attack,":[51],"an":[52],"onLine":[53],"muLtiple":[54],"normaLized":[55],"Gradient":[56],"Descent":[57],"(L3GD)":[58],"algorithm":[59,66],"is":[60,67,134],"proposed.":[61],"Under":[62],"mild":[63],"conditions,":[64],"proven":[68],"achieve":[70],"satisfactory":[71],"expected":[72],"dynamic":[73],"regret,":[74],"i.e,":[75],"<inline-formula":[76,83,93,100],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[77,84,94,101],"xmlns:xlink=\"http://www.w3.org/1999/xlink\"><tex-math":[78,85,95,102],"notation=\"LaTeX\">$\\mathcal":[79,86],"{O}({\\text{min}}":[80],"\\{{P_{T}^{*}}+{T^{\\frac{3}{4}},{S_{T}^{*}}+\\sqrt{T}}+{\\sum^{T}_{t=1}}||\u2207{f_{t}(x_{t}^{*})}||^{2}\\})$</tex-math></inline-formula>":[81],"and":[82,99,109,151,156],"{O}(F_{T}+T^{\\frac{3}{4}})$</tex-math></inline-formula>":[87],",":[88,98],"without":[89],"convex":[90],"assumption,":[91],"where":[92],"notation=\"LaTeX\">$P_T^*,":[96],"S_T^*$</tex-math></inline-formula>":[97],"notation=\"LaTeX\">$F_T$</tex-math></inline-formula>":[103],"denote":[104],"path-length,":[106,108],"squared":[107],"functional":[111],"variation,":[112],"respectively.":[113],"The":[114],"results":[115],"are":[116],"comparable":[117],"state-of-the-art":[119],"absence":[123],"our":[129],"best":[130],"knowledge,":[131],"first":[136],"consider":[138],"attacks":[141],"optimization.":[144],"Simulations":[145],"conducted":[146],"both":[148],"synthetic":[149],"examples":[150],"real-world":[152],"datasets,":[153],"namely":[154],"MNIST":[155],"CIFAR-10,":[157],"corroborate":[158],"resilience":[160],"L3GD.":[162]},"counts_by_year":[{"year":2024,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}