{"id":"https://openalex.org/W2902020649","doi":"https://doi.org/10.1109/globalsip.2018.8646618","title":"ZEROTH-ORDER STOCHASTIC PROJECTED GRADIENT DESCENT FOR NONCONVEX OPTIMIZATION","display_name":"ZEROTH-ORDER STOCHASTIC PROJECTED GRADIENT DESCENT FOR NONCONVEX OPTIMIZATION","publication_year":2018,"publication_date":"2018-11-01","ids":{"openalex":"https://openalex.org/W2902020649","doi":"https://doi.org/10.1109/globalsip.2018.8646618","mag":"2902020649"},"language":"en","primary_location":{"id":"doi:10.1109/globalsip.2018.8646618","is_oa":false,"landing_page_url":"https://doi.org/10.1109/globalsip.2018.8646618","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2018 IEEE Global Conference on Signal and Information Processing (GlobalSIP)","raw_type":"proceedings-article"},"type":"conference-paper","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/A5100321843","display_name":"Sijia Liu","orcid":"https://orcid.org/0000-0003-2817-6991"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sijia Liu","raw_affiliation_strings":["MIT-IBM Watson AI Lab, IBM Research"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"MIT-IBM Watson AI Lab, IBM Research","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103336011","display_name":"Xingguo Li","orcid":null},"institutions":[{"id":"https://openalex.org/I130238516","display_name":"University of Minnesota","ror":"https://ror.org/017zqws13","country_code":"US","type":"education","lineage":["https://openalex.org/I130238516"]},{"id":"https://openalex.org/I4210101327","display_name":"Twin Cities Orthopedics","ror":"https://ror.org/01en4s460","country_code":"US","type":"healthcare","lineage":["https://openalex.org/I4210101327"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Xingguo Li","raw_affiliation_strings":["University of Minnesota, Twin Cities"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Minnesota, Twin Cities","institution_ids":["https://openalex.org/I130238516","https://openalex.org/I4210101327"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5050344371","display_name":"Pin\u2010Yu Chen","orcid":"https://orcid.org/0000-0003-1039-8369"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Pin-Yu Chen","raw_affiliation_strings":["MIT-IBM Watson AI Lab, IBM Research"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"MIT-IBM Watson AI Lab, IBM Research","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5011305900","display_name":"Jarvis Haupt","orcid":"https://orcid.org/0000-0002-1570-7071"},"institutions":[{"id":"https://openalex.org/I130238516","display_name":"University of Minnesota","ror":"https://ror.org/017zqws13","country_code":"US","type":"education","lineage":["https://openalex.org/I130238516"]},{"id":"https://openalex.org/I4210101327","display_name":"Twin Cities Orthopedics","ror":"https://ror.org/01en4s460","country_code":"US","type":"healthcare","lineage":["https://openalex.org/I4210101327"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jarvis Haupt","raw_affiliation_strings":["University of Minnesota, Twin Cities"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Minnesota, Twin Cities","institution_ids":["https://openalex.org/I130238516","https://openalex.org/I4210101327"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5082560633","display_name":"Lisa Amini","orcid":"https://orcid.org/0000-0001-9097-0497"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lisa Amini","raw_affiliation_strings":["MIT-IBM Watson AI Lab, IBM Research"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"MIT-IBM Watson AI Lab, IBM Research","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.245,"has_fulltext":false,"cited_by_count":41,"citation_normalized_percentile":{"value":0.85423984,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"1179","last_page":"1183"},"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":0.9998000264167786,"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/T11307","display_name":"Domain Adaptation and Few-Shot Learning","score":0.9966999888420105,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/stochastic-gradient-descent","display_name":"Stochastic gradient descent","score":0.6637600660324097},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6470234394073486},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.6164076328277588},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.5878504514694214},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.531414806842804},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5259892344474792},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.46890154480934143},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.4673882722854614},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.46643948554992676},{"id":"https://openalex.org/keywords/stochastic-optimization","display_name":"Stochastic optimization","score":0.4535851776599884},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.45037731528282166},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.445056289434433},{"id":"https://openalex.org/keywords/proximal-gradient-methods","display_name":"Proximal Gradient Methods","score":0.4227864444255829},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.40111449360847473},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3630084991455078},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1780635118484497},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.16557636857032776},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.13104599714279175},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.09282612800598145}],"concepts":[{"id":"https://openalex.org/C206688291","wikidata":"https://www.wikidata.org/wiki/Q7617819","display_name":"Stochastic gradient descent","level":3,"score":0.6637600660324097},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6470234394073486},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.6164076328277588},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.5878504514694214},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.531414806842804},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5259892344474792},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.46890154480934143},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.4673882722854614},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.46643948554992676},{"id":"https://openalex.org/C194387892","wikidata":"https://www.wikidata.org/wiki/Q1747770","display_name":"Stochastic optimization","level":2,"score":0.4535851776599884},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.45037731528282166},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.445056289434433},{"id":"https://openalex.org/C10494615","wikidata":"https://www.wikidata.org/wiki/Q17086765","display_name":"Proximal Gradient Methods","level":4,"score":0.4227864444255829},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.40111449360847473},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3630084991455078},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1780635118484497},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.16557636857032776},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.13104599714279175},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09282612800598145},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","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},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","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/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/globalsip.2018.8646618","is_oa":false,"landing_page_url":"https://doi.org/10.1109/globalsip.2018.8646618","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2018 IEEE Global Conference on Signal and Information Processing (GlobalSIP)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":39,"referenced_works":["https://openalex.org/W153281708","https://openalex.org/W2029463628","https://openalex.org/W2149479912","https://openalex.org/W2161149069","https://openalex.org/W2171830216","https://openalex.org/W2410733619","https://openalex.org/W2556623528","https://openalex.org/W2603766943","https://openalex.org/W2742141334","https://openalex.org/W2746600820","https://openalex.org/W2765166321","https://openalex.org/W2772283936","https://openalex.org/W2772692493","https://openalex.org/W2803300317","https://openalex.org/W2807044327","https://openalex.org/W2963030777","https://openalex.org/W2963243330","https://openalex.org/W2963308146","https://openalex.org/W2963470657","https://openalex.org/W2963483475","https://openalex.org/W2963746283","https://openalex.org/W2964205597","https://openalex.org/W2964253222","https://openalex.org/W3106412272","https://openalex.org/W3124367822","https://openalex.org/W4293846201","https://openalex.org/W6606291809","https://openalex.org/W6638826736","https://openalex.org/W6681845865","https://openalex.org/W6683997977","https://openalex.org/W6714879114","https://openalex.org/W6730130278","https://openalex.org/W6739868092","https://openalex.org/W6741886682","https://openalex.org/W6745302534","https://openalex.org/W6746746554","https://openalex.org/W6751777967","https://openalex.org/W6751811190","https://openalex.org/W6752063739"],"related_works":["https://openalex.org/W4206903459","https://openalex.org/W2754816816","https://openalex.org/W4366280654","https://openalex.org/W3160167280","https://openalex.org/W4362706668","https://openalex.org/W4231621013","https://openalex.org/W3171021120","https://openalex.org/W3008318776","https://openalex.org/W4286899070","https://openalex.org/W4224283687"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,104],"analyze":[4],"the":[5,8,73,80,85,97,121,132],"convergence":[6,63,110,133],"of":[7,37,75,87,99,135],"zeroth-order":[9,136],"stochastic":[10],"projected":[11],"gradient":[12,41,92],"descent":[13],"(ZO-SPGD)":[14],"method":[15],"for":[16,65,91],"constrained":[17],"convex":[18,66],"and":[19,94],"nonconvex":[20,102],"optimization":[21,76],"scenarios":[22],"where":[23,70],"only":[24],"objective":[25],"function":[26],"values":[27],"(not":[28],"gradients)":[29],"are":[30],"directly":[31],"available.":[32],"We":[33,54],"show":[34,105],"statistical":[35],"properties":[36],"a":[38,50,59,127],"new":[39],"random":[40,45,88],"estimator,":[42],"constructed":[43],"through":[44],"direction":[46,89],"samples":[47,90],"drawn":[48],"from":[49],"bounded":[51],"uniform":[52],"distribution.":[53],"prove":[55],"that":[56,106],"ZO-SPGD":[57,107,125],"yields":[58],"O(d/(bq\u221aT)":[60],"+":[61,117],"1/\u221aT)":[62],"rate":[64,111,134],"but":[67,112],"non-smooth":[68],"optimization,":[69,103],"d":[71],"is":[72,79,84,96],"number":[74,86,98],"variables,":[77],"b":[78],"minibatch":[81],"size,":[82],"q":[83],"estimation,":[93],"T":[95],"iterations.":[100],"For":[101],"achieves":[108],"O(1/\u221aT)":[109],"suffers":[113],"an":[114],"additional":[115],"O((d":[116],"q)/(bq))":[118],"error.":[119],"Our":[120],"oretical":[122],"investigation":[123],"on":[124],"provides":[126],"general":[128],"framework":[129],"to":[130],"study":[131],"algorithms.":[137]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":8},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":10},{"year":2021,"cited_by_count":8},{"year":2020,"cited_by_count":3}],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2025-10-10T00:00:00"}
