{"id":"https://openalex.org/W3014120224","doi":"https://doi.org/10.1109/isit45174.2021.9517799","title":"Information-theoretic lower bounds for zero-order stochastic gradient estimation","display_name":"Information-theoretic lower bounds for zero-order stochastic gradient estimation","publication_year":2021,"publication_date":"2021-07-12","ids":{"openalex":"https://openalex.org/W3014120224","doi":"https://doi.org/10.1109/isit45174.2021.9517799","mag":"3014120224"},"language":"en","primary_location":{"id":"doi:10.1109/isit45174.2021.9517799","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit45174.2021.9517799","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2021 IEEE International Symposium on Information Theory (ISIT)","raw_type":"proceedings-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2003.13881","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5112348954","display_name":"Abdulrahman Alabdulkareem","orcid":null},"institutions":[{"id":"https://openalex.org/I219193219","display_name":"Purdue University West Lafayette","ror":"https://ror.org/02dqehb95","country_code":"US","type":"education","lineage":["https://openalex.org/I219193219"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Abdulrahman Alabdulkareem","raw_affiliation_strings":["Purdue University,Department of Computer Science,West Lafayette,IN,USA,47907","PURDUE UNIVERSITY"],"affiliations":[{"raw_affiliation_string":"Purdue University,Department of Computer Science,West Lafayette,IN,USA,47907","institution_ids":["https://openalex.org/I219193219"]},{"raw_affiliation_string":"PURDUE UNIVERSITY","institution_ids":["https://openalex.org/I219193219"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5038965118","display_name":"Jean Honorio","orcid":"https://orcid.org/0000-0002-6448-0598"},"institutions":[{"id":"https://openalex.org/I219193219","display_name":"Purdue University West Lafayette","ror":"https://ror.org/02dqehb95","country_code":"US","type":"education","lineage":["https://openalex.org/I219193219"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jean Honorio","raw_affiliation_strings":["Purdue University,Department of Computer Science,West Lafayette,IN,USA,47907","PURDUE UNIVERSITY"],"affiliations":[{"raw_affiliation_string":"Purdue University,Department of Computer Science,West Lafayette,IN,USA,47907","institution_ids":["https://openalex.org/I219193219"]},{"raw_affiliation_string":"PURDUE UNIVERSITY","institution_ids":["https://openalex.org/I219193219"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5112348954"],"corresponding_institution_ids":["https://openalex.org/I219193219"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.01280248,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"2316","last_page":"2321"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12101","display_name":"Advanced Bandit Algorithms Research","score":0.9983999729156494,"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/T11413","display_name":"Risk and Portfolio Optimization","score":0.998199999332428,"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/mathematics","display_name":"Mathematics","score":0.7695086598396301},{"id":"https://openalex.org/keywords/minimax","display_name":"Minimax","score":0.7000287771224976},{"id":"https://openalex.org/keywords/zero","display_name":"Zero (linguistics)","score":0.6770110130310059},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.670674204826355},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.6270631551742554},{"id":"https://openalex.org/keywords/oracle","display_name":"Oracle","score":0.6033705472946167},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5803402066230774},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.5780390501022339},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5492496490478516},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5457044839859009},{"id":"https://openalex.org/keywords/bounded-variation","display_name":"Bounded variation","score":0.5040103793144226},{"id":"https://openalex.org/keywords/gaussian-measure","display_name":"Gaussian measure","score":0.48027920722961426},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4470413327217102},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.4267251491546631},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.4232668876647949},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.3195788860321045},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3171783685684204},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.30633512139320374},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.267697274684906},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1148989200592041},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.1145433783531189},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07890439033508301}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7695086598396301},{"id":"https://openalex.org/C149728462","wikidata":"https://www.wikidata.org/wiki/Q751319","display_name":"Minimax","level":2,"score":0.7000287771224976},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.6770110130310059},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.670674204826355},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.6270631551742554},{"id":"https://openalex.org/C55166926","wikidata":"https://www.wikidata.org/wiki/Q2892946","display_name":"Oracle","level":2,"score":0.6033705472946167},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5803402066230774},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.5780390501022339},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5492496490478516},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5457044839859009},{"id":"https://openalex.org/C27851653","wikidata":"https://www.wikidata.org/wiki/Q829653","display_name":"Bounded variation","level":2,"score":0.5040103793144226},{"id":"https://openalex.org/C2777630202","wikidata":"https://www.wikidata.org/wiki/Q5527840","display_name":"Gaussian measure","level":3,"score":0.48027920722961426},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4470413327217102},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4267251491546631},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.4232668876647949},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.3195788860321045},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3171783685684204},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.30633512139320374},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.267697274684906},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1148989200592041},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.1145433783531189},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07890439033508301},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"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/C115903868","wikidata":"https://www.wikidata.org/wiki/Q80993","display_name":"Software engineering","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/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1109/isit45174.2021.9517799","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit45174.2021.9517799","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2021 IEEE International Symposium on Information Theory (ISIT)","raw_type":"proceedings-article"},{"id":"pmh:oai:arXiv.org:2003.13881","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2003.13881","pdf_url":"https://arxiv.org/pdf/2003.13881","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":null,"raw_type":"text"},{"id":"mag:3014120224","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/2003.13881.pdf","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.2003.13881","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2003.13881","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2003.13881","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2003.13881","pdf_url":"https://arxiv.org/pdf/2003.13881","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":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3014120224.pdf","grobid_xml":"https://content.openalex.org/works/W3014120224.grobid-xml"},"referenced_works_count":23,"referenced_works":["https://openalex.org/W1538452572","https://openalex.org/W1571975558","https://openalex.org/W1646152356","https://openalex.org/W2096698247","https://openalex.org/W2096840748","https://openalex.org/W2108829665","https://openalex.org/W2121591532","https://openalex.org/W2134443838","https://openalex.org/W2155027007","https://openalex.org/W2167816765","https://openalex.org/W2171830216","https://openalex.org/W2173041192","https://openalex.org/W2551284144","https://openalex.org/W2953013790","https://openalex.org/W2963912441","https://openalex.org/W2964182380","https://openalex.org/W3141990068","https://openalex.org/W4211030719","https://openalex.org/W6636774829","https://openalex.org/W6678454853","https://openalex.org/W6683204974","https://openalex.org/W6685362935","https://openalex.org/W6748305792"],"related_works":["https://openalex.org/W3131517864","https://openalex.org/W2949728505","https://openalex.org/W1546740833","https://openalex.org/W3041459315","https://openalex.org/W2159700154","https://openalex.org/W2963453778","https://openalex.org/W1657403998","https://openalex.org/W3178405068","https://openalex.org/W2616771963","https://openalex.org/W3206696270","https://openalex.org/W2726456371","https://openalex.org/W2963296412","https://openalex.org/W1878857172","https://openalex.org/W2498858925","https://openalex.org/W2087600519","https://openalex.org/W3039426095","https://openalex.org/W1822292100","https://openalex.org/W1629135078","https://openalex.org/W2962957329","https://openalex.org/W3005747921"],"abstract_inverted_index":{"In":[0,27],"this":[1,28,147],"paper":[2,148],"we":[3],"analyze":[4],"the":[5,12,38,44,47,55,61,89,122,136],"necessary":[6],"number":[7,57],"of":[8,14,37,46,58,138,146],"samples":[9,59,76],"to":[10,34,42],"estimate":[11,45],"gradient":[13,140],"any":[15],"multidimensional":[16],"smooth":[17],"(possibly":[18],"non-convex)":[19],"function":[20],"in":[21,40,68],"a":[22,65,94],"zero-order":[23],"stochastic":[24],"oracle":[25,96],"model.":[26],"model,":[29],"an":[30,52],"estimator":[31],"has":[32,97],"access":[33],"noisy":[35],"values":[36],"function,":[39],"order":[41,112],"produce":[43],"gradient.":[48],"We":[49,86],"also":[50],"provide":[51],"analysis":[53],"on":[54],"sufficient":[56],"for":[60,93,105,118,135],"finite":[62,90,123],"difference":[63,91,124],"method,":[64],"classical":[66],"technique":[67],"numerical":[69],"linear":[70],"algebra.":[71],"For":[72],"<tex":[73],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[74,101],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">$T$</tex>":[75],"and":[77,110,130],"d":[78],"dimensions,":[79],"our":[80],"information-theoretic":[81],"lower":[82],"bound":[83],"is":[84,126,133,149],"\u03a9(\u221ad/T).":[85],"show":[87],"that":[88],"method":[92,125],"bounded-variance":[95],"rate":[98],"O(d":[99],"<sup":[100],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">4/3</sup>":[102],"/":[103],"\u221aT)":[104],"functions":[106],"with":[107],"zero":[108],"third":[109],"higher":[111],"derivatives.":[113],"These":[114],"rates":[115],"are":[116],"tight":[117],"Gaussian":[119],"oracles.":[120],"Thus,":[121],"not":[127],"minimax":[128],"optimal,":[129],"therefore":[131],"there":[132],"space":[134],"development":[137],"better":[139],"estimation":[141],"methods.":[142],"A":[143],"full":[144],"version":[145],"accessible":[150],"at:":[151],"https://arxiv.org/pdf/2003.13881.pdf":[152]},"counts_by_year":[],"updated_date":"2026-03-25T13:04:00.132906","created_date":"2025-10-10T00:00:00"}
