{"id":"https://openalex.org/W4382935866","doi":"https://doi.org/10.23919/acc55779.2023.10156450","title":"An Almost Sure Convergence Analysis of Zeroth-Order Mirror Descent Algorithm","display_name":"An Almost Sure Convergence Analysis of Zeroth-Order Mirror Descent Algorithm","publication_year":2023,"publication_date":"2023-05-31","ids":{"openalex":"https://openalex.org/W4382935866","doi":"https://doi.org/10.23919/acc55779.2023.10156450"},"language":"en","primary_location":{"id":"doi:10.23919/acc55779.2023.10156450","is_oa":false,"landing_page_url":"http://dx.doi.org/10.23919/acc55779.2023.10156450","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2023 American Control Conference (ACC)","raw_type":"proceedings-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/A5088208382","display_name":"Anik Kumar Paul","orcid":"https://orcid.org/0000-0001-6206-5932"},"institutions":[{"id":"https://openalex.org/I24676775","display_name":"Indian Institute of Technology Madras","ror":"https://ror.org/03v0r5n49","country_code":"IN","type":"education","lineage":["https://openalex.org/I24676775"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Anik Kumar Paul","raw_affiliation_strings":["IIT Madras,Department of Electrical Engineering,Chennai,India,600036"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"IIT Madras,Department of Electrical Engineering,Chennai,India,600036","institution_ids":["https://openalex.org/I24676775"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5059111533","display_name":"Arun D. Mahindrakar","orcid":"https://orcid.org/0000-0002-7866-4363"},"institutions":[{"id":"https://openalex.org/I24676775","display_name":"Indian Institute of Technology Madras","ror":"https://ror.org/03v0r5n49","country_code":"IN","type":"education","lineage":["https://openalex.org/I24676775"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Arun D Mahindrakar","raw_affiliation_strings":["Indian Institute of Technology Madras,Department of Electrical Engineering,Chennai,India,600036"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Indian Institute of Technology Madras,Department of Electrical Engineering,Chennai,India,600036","institution_ids":["https://openalex.org/I24676775"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5025105353","display_name":"Rachel Kalpana Kalaimani","orcid":"https://orcid.org/0000-0002-0701-7927"},"institutions":[{"id":"https://openalex.org/I24676775","display_name":"Indian Institute of Technology Madras","ror":"https://ror.org/03v0r5n49","country_code":"IN","type":"education","lineage":["https://openalex.org/I24676775"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Rachel K Kalaimani","raw_affiliation_strings":["Indian Institute of Technology Madras,Department of Electrical Engineering,Chennai,India,600036"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Indian Institute of Technology Madras,Department of Electrical Engineering,Chennai,India,600036","institution_ids":["https://openalex.org/I24676775"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.3263,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.63790191,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":null,"issue":null,"first_page":"855","last_page":"860"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":1.0,"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":1.0,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10249","display_name":"Distributed Control Multi-Agent Systems","score":0.9968000054359436,"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/iterated-function","display_name":"Iterated function","score":0.7668642997741699},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6592886447906494},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.6446638703346252},{"id":"https://openalex.org/keywords/descent","display_name":"Descent (aeronautics)","score":0.5830651521682739},{"id":"https://openalex.org/keywords/zeroth-law-of-thermodynamics","display_name":"Zeroth law of thermodynamics","score":0.5743558406829834},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.561718225479126},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5365567207336426},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5243195295333862},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.4746426045894623},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.45182156562805176},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.443654328584671},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.34386441111564636},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3305191099643707},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1260291039943695},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07253226637840271},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07117104530334473},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.0704488456249237}],"concepts":[{"id":"https://openalex.org/C140479938","wikidata":"https://www.wikidata.org/wiki/Q5254619","display_name":"Iterated function","level":2,"score":0.7668642997741699},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6592886447906494},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6446638703346252},{"id":"https://openalex.org/C2776637919","wikidata":"https://www.wikidata.org/wiki/Q624380","display_name":"Descent (aeronautics)","level":2,"score":0.5830651521682739},{"id":"https://openalex.org/C68755742","wikidata":"https://www.wikidata.org/wiki/Q190983","display_name":"Zeroth law of thermodynamics","level":2,"score":0.5743558406829834},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.561718225479126},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5365567207336426},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5243195295333862},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.4746426045894623},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.45182156562805176},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.443654328584671},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.34386441111564636},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3305191099643707},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1260291039943695},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07253226637840271},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07117104530334473},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0704488456249237},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C153294291","wikidata":"https://www.wikidata.org/wiki/Q25261","display_name":"Meteorology","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"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},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.23919/acc55779.2023.10156450","is_oa":false,"landing_page_url":"http://dx.doi.org/10.23919/acc55779.2023.10156450","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2023 American Control Conference (ACC)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W1604467579","https://openalex.org/W1998880679","https://openalex.org/W2114973703","https://openalex.org/W2149479912","https://openalex.org/W2497446532","https://openalex.org/W2912098123","https://openalex.org/W2942536919","https://openalex.org/W2963470657","https://openalex.org/W2963910188","https://openalex.org/W2969507060","https://openalex.org/W3083021344","https://openalex.org/W3096577336","https://openalex.org/W3158102619","https://openalex.org/W3161862726","https://openalex.org/W4205841652","https://openalex.org/W4206742934","https://openalex.org/W6795531353"],"related_works":["https://openalex.org/W2798687591","https://openalex.org/W2486267010","https://openalex.org/W4297745082","https://openalex.org/W2055832495","https://openalex.org/W1601218205","https://openalex.org/W2793511430","https://openalex.org/W1993876517","https://openalex.org/W2014930628","https://openalex.org/W2015288657","https://openalex.org/W4313177131"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3],"show":[4],"almost":[5,62],"sure":[6],"convergence":[7],"of":[8,24,42,47,50,57,72],"zeroth-order":[9,74],"mirror":[10,75],"descent":[11,76],"algorithm.":[12,77],"The":[13],"algorithm":[14,52],"admits":[15],"non-smooth":[16],"convex":[17],"functions":[18],"and":[19],"assumes":[20],"only":[21],"an":[22],"estimate":[23],"the":[25,44,48,51,58,66,69,73],"gradient":[26],"is":[27],"available,":[28],"obtained":[29],"using":[30],"Nesterov\u2019s":[31],"Gausssian":[32],"Approximation":[33],"technique":[34],"(NGA).":[35],"We":[36,64],"establish":[37],"that":[38],"under":[39],"suitable":[40],"condition":[41],"step-size,":[43],"function":[45,60],"value":[46,61],"iterates":[49],"converge":[53],"to":[54,68],"a":[55],"neighborhood":[56],"optimal":[59],"surely.":[63],"extend":[65],"analysis":[67],"distributed":[70],"implementation":[71]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}