{"id":"https://openalex.org/W3134040281","doi":"https://doi.org/10.1137/22m1510261","title":"Small Errors in Random Zeroth-Order Optimization Are Imaginary","display_name":"Small Errors in Random Zeroth-Order Optimization Are Imaginary","publication_year":2024,"publication_date":"2024-07-19","ids":{"openalex":"https://openalex.org/W3134040281","doi":"https://doi.org/10.1137/22m1510261","mag":"3134040281"},"language":"en","primary_location":{"id":"doi:10.1137/22m1510261","is_oa":false,"landing_page_url":"https://doi.org/10.1137/22m1510261","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Optimization","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2103.05478","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5020343130","display_name":"Wouter Jongeneel","orcid":"https://orcid.org/0000-0002-0078-9596"},"institutions":[{"id":"https://openalex.org/I5124864","display_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","ror":"https://ror.org/02s376052","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I5124864"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Wouter Jongeneel","raw_affiliation_strings":["Risk Analytics and Optimization Chair, \u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne, 1015 Lausanne, Switzerland"],"raw_orcid":"https://orcid.org/0000-0002-0078-9596","affiliations":[{"raw_affiliation_string":"Risk Analytics and Optimization Chair, \u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne, 1015 Lausanne, Switzerland","institution_ids":["https://openalex.org/I5124864"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5041884309","display_name":"Man\u2013Chung Yue","orcid":"https://orcid.org/0000-0002-7992-9490"},"institutions":[{"id":"https://openalex.org/I4210114340","display_name":"Istituto di Scienze Marine del Consiglio Nazionale delle Ricerche","ror":"https://ror.org/02hdf6119","country_code":"IT","type":"facility","lineage":["https://openalex.org/I4210114340","https://openalex.org/I4210155236"]},{"id":"https://openalex.org/I889458895","display_name":"University of Hong Kong","ror":"https://ror.org/02zhqgq86","country_code":"HK","type":"education","lineage":["https://openalex.org/I889458895"]}],"countries":["HK","IT"],"is_corresponding":false,"raw_author_name":"Man-Chung Yue","raw_affiliation_strings":["Musketeers Foundation Institute of Data Science and Department of Industrial and Manufacturing Systems Engineering, The University of Hong Kong, Hong Kong"],"raw_orcid":"https://orcid.org/0000-0002-7992-9490","affiliations":[{"raw_affiliation_string":"Musketeers Foundation Institute of Data Science and Department of Industrial and Manufacturing Systems Engineering, The University of Hong Kong, Hong Kong","institution_ids":["https://openalex.org/I4210114340","https://openalex.org/I889458895"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5065780980","display_name":"Daniel K\u00fchn","orcid":"https://orcid.org/0000-0003-2697-8886"},"institutions":[{"id":"https://openalex.org/I5124864","display_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","ror":"https://ror.org/02s376052","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I5124864"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Daniel Kuhn","raw_affiliation_strings":["Risk Analytics and Optimization Chair, \u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne, 1015 Lausanne, Switzerland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Risk Analytics and Optimization Chair, \u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne, 1015 Lausanne, Switzerland","institution_ids":["https://openalex.org/I5124864"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.3003,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.44822172,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"34","issue":"3","first_page":"2638","last_page":"2670"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9998000264167786,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9998000264167786,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/smoothing","display_name":"Smoothing","score":0.7776192426681519},{"id":"https://openalex.org/keywords/zeroth-law-of-thermodynamics","display_name":"Zeroth law of thermodynamics","score":0.6443802714347839},{"id":"https://openalex.org/keywords/sublinear-function","display_name":"Sublinear function","score":0.6391608715057373},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5398982763290405},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.539879560470581},{"id":"https://openalex.org/keywords/approximation-error","display_name":"Approximation error","score":0.524383008480072},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4753665328025818},{"id":"https://openalex.org/keywords/approximation-algorithm","display_name":"Approximation algorithm","score":0.4670620858669281},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.40522438287734985},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3855755031108856},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3406509757041931},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.25585317611694336},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.16428717970848083},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.07413876056671143}],"concepts":[{"id":"https://openalex.org/C3770464","wikidata":"https://www.wikidata.org/wiki/Q775963","display_name":"Smoothing","level":2,"score":0.7776192426681519},{"id":"https://openalex.org/C68755742","wikidata":"https://www.wikidata.org/wiki/Q190983","display_name":"Zeroth law of thermodynamics","level":2,"score":0.6443802714347839},{"id":"https://openalex.org/C117160843","wikidata":"https://www.wikidata.org/wiki/Q338652","display_name":"Sublinear function","level":2,"score":0.6391608715057373},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5398982763290405},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.539879560470581},{"id":"https://openalex.org/C122383733","wikidata":"https://www.wikidata.org/wiki/Q865920","display_name":"Approximation error","level":2,"score":0.524383008480072},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4753665328025818},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.4670620858669281},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.40522438287734985},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3855755031108856},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3406509757041931},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.25585317611694336},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.16428717970848083},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.07413876056671143},{"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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","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}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/22m1510261","is_oa":false,"landing_page_url":"https://doi.org/10.1137/22m1510261","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Optimization","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2103.05478","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2103.05478","pdf_url":"https://arxiv.org/pdf/2103.05478","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"pmh:oai:hub.hku.hk:10722/346072","is_oa":true,"landing_page_url":"https://hub.hku.hk/handle/10722/346072","pdf_url":"http://hub.hku.hk/bitstream/10722/346072/1/content.pdf","source":{"id":"https://openalex.org/S4377196271","display_name":"The HKU Scholars Hub (University of Hong Kong)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I889458895","host_organization_name":"University of Hong Kong","host_organization_lineage":["https://openalex.org/I889458895"],"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":"Article"},{"id":"pmh:oai:infoscience.epfl.ch:295393","is_oa":true,"landing_page_url":"http://infoscience.epfl.ch/record/295393","pdf_url":null,"source":{"id":"https://openalex.org/S4306400487","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","issn_l":null,"issn":null,"is_oa":true,"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-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://infoscience.epfl.ch/record/295393","raw_type":null}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2103.05478","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2103.05478","pdf_url":"https://arxiv.org/pdf/2103.05478","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2179010935","display_name":"NCCR Automation: Dependable Ubiquitous Automation","funder_award_id":"180545","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"},{"id":"https://openalex.org/G5129771594","display_name":null,"funder_award_id":"180545","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6590829305","display_name":null,"funder_award_id":"51NF40 180545","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320320924","display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung","ror":"https://ror.org/00yjd3n13"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":89,"referenced_works":["https://openalex.org/W146900863","https://openalex.org/W161930422","https://openalex.org/W181733065","https://openalex.org/W1488781340","https://openalex.org/W1495395477","https://openalex.org/W1499021337","https://openalex.org/W1505731132","https://openalex.org/W1533404702","https://openalex.org/W1557324374","https://openalex.org/W1557899381","https://openalex.org/W1594563152","https://openalex.org/W1597216993","https://openalex.org/W1969551552","https://openalex.org/W1984068279","https://openalex.org/W1984997253","https://openalex.org/W1987941491","https://openalex.org/W2006962396","https://openalex.org/W2009797711","https://openalex.org/W2024040438","https://openalex.org/W2043458938","https://openalex.org/W2091638851","https://openalex.org/W2098918617","https://openalex.org/W2106713925","https://openalex.org/W2120575449","https://openalex.org/W2121210949","https://openalex.org/W2124289529","https://openalex.org/W2124768887","https://openalex.org/W2149479912","https://openalex.org/W2151056989","https://openalex.org/W2159930037","https://openalex.org/W2164449950","https://openalex.org/W2168914046","https://openalex.org/W2171074980","https://openalex.org/W2171830216","https://openalex.org/W2188503328","https://openalex.org/W2323326317","https://openalex.org/W2466924381","https://openalex.org/W2478429860","https://openalex.org/W2529465479","https://openalex.org/W2536620281","https://openalex.org/W2586930666","https://openalex.org/W2588453247","https://openalex.org/W2604272474","https://openalex.org/W2626106585","https://openalex.org/W2745281314","https://openalex.org/W2772124661","https://openalex.org/W2775085189","https://openalex.org/W2791375846","https://openalex.org/W2793948820","https://openalex.org/W2800363843","https://openalex.org/W2886474253","https://openalex.org/W2904304778","https://openalex.org/W2908776022","https://openalex.org/W2941034199","https://openalex.org/W2945204933","https://openalex.org/W2952840318","https://openalex.org/W2962782524","https://openalex.org/W2963062786","https://openalex.org/W2963308146","https://openalex.org/W2963470657","https://openalex.org/W2963477800","https://openalex.org/W2963483475","https://openalex.org/W2963819344","https://openalex.org/W2979411530","https://openalex.org/W2986078788","https://openalex.org/W3035736653","https://openalex.org/W3036279995","https://openalex.org/W3083021344","https://openalex.org/W3087723685","https://openalex.org/W3094766279","https://openalex.org/W3102143361","https://openalex.org/W3120373191","https://openalex.org/W3122422392","https://openalex.org/W3125612732","https://openalex.org/W3128780393","https://openalex.org/W3136297071","https://openalex.org/W3141595720","https://openalex.org/W3151861680","https://openalex.org/W3163478863","https://openalex.org/W3173141421","https://openalex.org/W3217389438","https://openalex.org/W4212774754","https://openalex.org/W4224990512","https://openalex.org/W4242080388","https://openalex.org/W4289767001","https://openalex.org/W4297093107","https://openalex.org/W4300059230","https://openalex.org/W4300448178","https://openalex.org/W4301435544"],"related_works":["https://openalex.org/W4376639521","https://openalex.org/W2110817230","https://openalex.org/W3091355678","https://openalex.org/W1606488336","https://openalex.org/W1988569331","https://openalex.org/W189995875","https://openalex.org/W4255193494","https://openalex.org/W2284958355","https://openalex.org/W2962894463","https://openalex.org/W4301487118"],"abstract_inverted_index":{"Most":[0],"zeroth-order":[1,192],"optimization":[2],"algorithms":[3,193],"mimic":[4],"a":[5,26,44,65,74,83,91,144,152],"first-order":[6],"algorithm":[7],"but":[8],"replace":[9],"the":[10,13,41,48,55,95,116,135,139,149,162,199,205],"gradient":[11,19,42,145],"of":[12,29,43,47,68,77,94,161],"objective":[14,49,136,150],"function":[15,30,50,69,85,113,137,171],"with":[16],"some":[17],"noisy":[18],"estimator":[20,33,146,167,197],"that":[21,147,191,194,212],"can":[22,87],"be":[23,88],"computed":[24],"from":[25,73,98,120],"small":[27,158],"number":[28,67],"evaluations.":[31],"This":[32],"is":[34,60,174],"constructed":[35],"randomly,":[36],"and":[37,142],"its":[38,180],"expectation":[39],"matches":[40],"smooth":[45],"approximation":[46],"whose":[51,155],"quality":[52],"improves":[53],"as":[54,104,184,204],"underlying":[56],"smoothing":[57],"parameter":[58],"\u03b4":[59,105,124,185],"reduced.":[61],"Gradient":[62],"estimators":[63,80],"requiring":[64],"smaller":[66],"evaluations":[70],"are":[71],"preferable":[72],"computational":[75],"point":[76,154],"view.":[78],"While":[79],"based":[81,110],"on":[82,111,115],"single":[84],"evaluation":[86],"obtained":[89],"by":[90],"clever":[92],"use":[93,195],"divergence":[96],"theorem":[97],"vector":[99],"calculus,":[100],"their":[101],"variance":[102,181],"explodes":[103],"tends":[106,125,186],"to":[107,126,138,176,187],"0.":[108,127,188],"Estimators":[109],"multiple":[112],"evaluations,":[114],"other":[117],"hand,":[118],"suffer":[119],"numerical":[121],"cancellation":[122],"when":[123],"To":[128],"combat":[129],"both":[130],"effects":[131],"simultaneously,":[132],"we":[133],"extend":[134],"complex":[140,153],"domain":[141],"construct":[143],"evaluates":[148],"at":[151],"coordinates":[156],"have":[157],"imaginary":[159],"parts":[160],"order":[163],"\u03b4.":[164],"As":[165],"this":[166],"requires":[168],"only":[169],"one":[170],"evaluation,":[172],"it":[173],"immune":[175],"cancellation.":[177],"In":[178],"addition,":[179],"remains":[182],"bounded":[183],"We":[189],"prove":[190],"our":[196],"offer":[198],"same":[200],"theoretical":[201],"convergence":[202],"guarantees":[203],"state-of-the-art":[206],"methods.":[207],"Numerical":[208],"experiments":[209],"suggest,":[210],"however,":[211],"they":[213],"often":[214],"converge":[215],"faster":[216],"in":[217],"practice.":[218]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2025-12-23T23:11:35.936235","created_date":"2025-10-10T00:00:00"}