{"id":"https://openalex.org/W2002517365","doi":"https://doi.org/10.1109/cdc.2012.6426698","title":"Randomized smoothing for (parallel) stochastic optimization","display_name":"Randomized smoothing for (parallel) stochastic optimization","publication_year":2012,"publication_date":"2012-12-01","ids":{"openalex":"https://openalex.org/W2002517365","doi":"https://doi.org/10.1109/cdc.2012.6426698","mag":"2002517365"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2012.6426698","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2012.6426698","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2012 IEEE 51st IEEE Conference on Decision and Control (CDC)","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://eprints.qut.edu.au/119121/17/1103.4296.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5061331093","display_name":"John C. Duchi","orcid":"https://orcid.org/0000-0003-0045-7185"},"institutions":[{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"John C. Duchi","raw_affiliation_strings":["Department of Electrical Engineering and Computer Science, University of California, Berkeley, Berkeley, CA, USA","Department of Electrical Engineering and Computer Science, UC Berkeley, CA 94720, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering and Computer Science, University of California, Berkeley, Berkeley, CA, USA","institution_ids":["https://openalex.org/I95457486"]},{"raw_affiliation_string":"Department of Electrical Engineering and Computer Science, UC Berkeley, CA 94720, USA","institution_ids":["https://openalex.org/I95457486"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5030261391","display_name":"Peter L. Bartlett","orcid":"https://orcid.org/0000-0002-8760-3140"},"institutions":[{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Peter L. Bartlett","raw_affiliation_strings":["Department of Electrical Engineering and Computer Science, University of California, Berkeley, Berkeley, CA, USA","Department of Electrical Engineering and Computer Science, UC Berkeley, CA 94720, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering and Computer Science, University of California, Berkeley, Berkeley, CA, USA","institution_ids":["https://openalex.org/I95457486"]},{"raw_affiliation_string":"Department of Electrical Engineering and Computer Science, UC Berkeley, CA 94720, USA","institution_ids":["https://openalex.org/I95457486"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5038379562","display_name":"Martin J. Wainwright","orcid":"https://orcid.org/0000-0002-8760-2236"},"institutions":[{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Martin J. Wainwright","raw_affiliation_strings":["Department of Electrical Engineering and Computer Science, Department of Statistics, University of California, Berkeley, Berkeley, CA, USA","Department of Electrical Engineering and Computer Science, UC Berkeley, CA 94720, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering and Computer Science, Department of Statistics, University of California, Berkeley, Berkeley, CA, USA","institution_ids":["https://openalex.org/I95457486"]},{"raw_affiliation_string":"Department of Electrical Engineering and Computer Science, UC Berkeley, CA 94720, USA","institution_ids":["https://openalex.org/I95457486"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5061331093"],"corresponding_institution_ids":["https://openalex.org/I95457486"],"apc_list":null,"apc_paid":null,"fwci":1.7686,"has_fulltext":false,"cited_by_count":97,"citation_normalized_percentile":{"value":0.86274721,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"5442","last_page":"5444"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9994000196456909,"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":0.9994000196456909,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.993399977684021,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T10136","display_name":"Statistical Methods and Inference","score":0.9918000102043152,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/stochastic-optimization","display_name":"Stochastic optimization","score":0.7762801051139832},{"id":"https://openalex.org/keywords/smoothing","display_name":"Smoothing","score":0.7573734521865845},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6585676074028015},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6069626808166504},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.6067829132080078},{"id":"https://openalex.org/keywords/variance","display_name":"Variance (accounting)","score":0.578538179397583},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.4590188264846802},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.31742897629737854},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2873018980026245}],"concepts":[{"id":"https://openalex.org/C194387892","wikidata":"https://www.wikidata.org/wiki/Q1747770","display_name":"Stochastic optimization","level":2,"score":0.7762801051139832},{"id":"https://openalex.org/C3770464","wikidata":"https://www.wikidata.org/wiki/Q775963","display_name":"Smoothing","level":2,"score":0.7573734521865845},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6585676074028015},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6069626808166504},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6067829132080078},{"id":"https://openalex.org/C196083921","wikidata":"https://www.wikidata.org/wiki/Q7915758","display_name":"Variance (accounting)","level":2,"score":0.578538179397583},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.4590188264846802},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.31742897629737854},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2873018980026245},{"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/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.0},{"id":"https://openalex.org/C144133560","wikidata":"https://www.wikidata.org/wiki/Q4830453","display_name":"Business","level":0,"score":0.0},{"id":"https://openalex.org/C121955636","wikidata":"https://www.wikidata.org/wiki/Q4116214","display_name":"Accounting","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":3,"locations":[{"id":"doi:10.1109/cdc.2012.6426698","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2012.6426698","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2012 IEEE 51st IEEE Conference on Decision and Control (CDC)","raw_type":"proceedings-article"},{"id":"pmh:oai:eprints.qut.edu.au:119121","is_oa":true,"landing_page_url":null,"pdf_url":"https://eprints.qut.edu.au/119121/17/1103.4296.pdf","source":{"id":"https://openalex.org/S4306402607","display_name":"QUT ePrints (Queensland University of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I160993911","host_organization_name":"Queensland University of Technology","host_organization_lineage":["https://openalex.org/I160993911"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Proceedings of the 2012 IEEE 51st Annual Conference on Decision and Control (CDC 2012)","raw_type":"Chapter in Book, Report or Conference volume"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.251.2718","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.251.2718","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.berkeley.edu/%7Ejduchi/projects/DuchiBaWa12_icml.pdf","raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:eprints.qut.edu.au:119121","is_oa":true,"landing_page_url":null,"pdf_url":"https://eprints.qut.edu.au/119121/17/1103.4296.pdf","source":{"id":"https://openalex.org/S4306402607","display_name":"QUT ePrints (Queensland University of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I160993911","host_organization_name":"Queensland University of Technology","host_organization_lineage":["https://openalex.org/I160993911"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Proceedings of the 2012 IEEE 51st Annual Conference on Decision and Control (CDC 2012)","raw_type":"Chapter in Book, Report or Conference volume"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5693069798","display_name":null,"funder_award_id":"09NL184","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G5921281487","display_name":null,"funder_award_id":"number","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6621079209","display_name":null,"funder_award_id":"NDSEG","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6894402473","display_name":null,"funder_award_id":"Fellowship","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7151194999","display_name":null,"funder_award_id":"NDSEG","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G848032724","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8501711393","display_name":"Regularization Methods for Online Learning","funder_award_id":"0830410","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8926491534","display_name":null,"funder_award_id":"Fellowship","funder_id":"https://openalex.org/F4320333566","funder_display_name":"National Defense Science and Engineering Graduate"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320333566","display_name":"National Defense Science and Engineering Graduate","ror":null},{"id":"https://openalex.org/F4320338279","display_name":"Air Force Office of Scientific Research","ror":"https://ror.org/011e9bt93"}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W2002517365.pdf"},"referenced_works_count":39,"referenced_works":["https://openalex.org/W131378802","https://openalex.org/W147273232","https://openalex.org/W1487404723","https://openalex.org/W1505731132","https://openalex.org/W1557994858","https://openalex.org/W1632114991","https://openalex.org/W1979134936","https://openalex.org/W1992208280","https://openalex.org/W2003677307","https://openalex.org/W2022255443","https://openalex.org/W2024484010","https://openalex.org/W2044001837","https://openalex.org/W2087771945","https://openalex.org/W2096199223","https://openalex.org/W2096840748","https://openalex.org/W2097826433","https://openalex.org/W2117154949","https://openalex.org/W2119821739","https://openalex.org/W2125993116","https://openalex.org/W2130062883","https://openalex.org/W2136360692","https://openalex.org/W2142623206","https://openalex.org/W2147632348","https://openalex.org/W2150102617","https://openalex.org/W2164301055","https://openalex.org/W2262174858","https://openalex.org/W2489822048","https://openalex.org/W2911796152","https://openalex.org/W2912388896","https://openalex.org/W2962720772","https://openalex.org/W2963912441","https://openalex.org/W2988806182","https://openalex.org/W3017285694","https://openalex.org/W3020882730","https://openalex.org/W4239510810","https://openalex.org/W4293456528","https://openalex.org/W4300167747","https://openalex.org/W6656719126","https://openalex.org/W6679314259"],"related_works":["https://openalex.org/W2361828096","https://openalex.org/W1978745259","https://openalex.org/W3127438322","https://openalex.org/W4287330080","https://openalex.org/W1990112656","https://openalex.org/W4283738289","https://openalex.org/W2363855676","https://openalex.org/W2152231846","https://openalex.org/W195464835","https://openalex.org/W193468460"],"abstract_inverted_index":{"By":[0],"combining":[1],"randomized":[2],"smoothing":[3],"techniques":[4,54],"with":[5,21,55],"accelerated":[6],"gradient":[7,33],"methods,":[8],"we":[9],"obtain":[10],"convergence":[11],"rates":[12,46],"for":[13,47],"stochastic":[14,64],"optimization":[15,60,65],"procedures,":[16],"both":[17],"in":[18],"expectation":[19],"and":[20],"high":[22],"probability,":[23],"that":[24],"have":[25],"optimal":[26],"dependence":[27],"on":[28,58],"the":[29,32,36,43,83,87,90],"variance":[30],"of":[31,38,52,70,86,92],"estimates.":[34],"To":[35],"best":[37],"our":[39,53,71,93],"knowledge,":[40],"these":[41],"are":[42],"first":[44],"variance-based":[45],"non-smooth":[48],"optimization.":[49],"A":[50],"combination":[51],"recent":[56],"work":[57],"decentralized":[59],"yields":[61],"order-optimal":[62],"parallel":[63],"algorithms.":[66,94],"We":[67],"give":[68],"applications":[69],"results":[72,81],"to":[73],"several":[74],"statistical":[75],"machine":[76],"learning":[77],"problems,":[78],"providing":[79],"experimental":[80],"(in":[82],"full":[84],"version":[85],"paper)":[88],"demonstrating":[89],"effectiveness":[91]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":9},{"year":2023,"cited_by_count":12},{"year":2022,"cited_by_count":13},{"year":2021,"cited_by_count":15},{"year":2020,"cited_by_count":8},{"year":2019,"cited_by_count":9},{"year":2018,"cited_by_count":12},{"year":2017,"cited_by_count":9},{"year":2016,"cited_by_count":2},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}