{"id":"https://openalex.org/W1548903454","doi":"https://doi.org/10.1007/3-540-44581-1_5","title":"A Sequential Approximation Bound for Some Sample-Dependent Convex Optimization Problems with Applications in Learning","display_name":"A Sequential Approximation Bound for Some Sample-Dependent Convex Optimization Problems with Applications in Learning","publication_year":2001,"publication_date":"2001-01-01","ids":{"openalex":"https://openalex.org/W1548903454","doi":"https://doi.org/10.1007/3-540-44581-1_5","mag":"1548903454"},"language":"en","primary_location":{"id":"doi:10.1007/3-540-44581-1_5","is_oa":false,"landing_page_url":"https://doi.org/10.1007/3-540-44581-1_5","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"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/A5100378783","display_name":"Tong Zhang","orcid":"https://orcid.org/0000-0002-3506-0180"},"institutions":[{"id":"https://openalex.org/I1341412227","display_name":"IBM (United States)","ror":"https://ror.org/05hh8d621","country_code":"US","type":"company","lineage":["https://openalex.org/I1341412227"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Tong Zhang","raw_affiliation_strings":["IBM T.J. Watson Research Center, Yorktown Heights, NY, 10598"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"IBM T.J. Watson Research Center, Yorktown Heights, NY, 10598","institution_ids":["https://openalex.org/I1341412227"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5100378783"],"corresponding_institution_ids":["https://openalex.org/I1341412227"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"65","last_page":"81"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9997000098228455,"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":0.9997000098228455,"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/T12101","display_name":"Advanced Bandit Algorithms Research","score":0.9995999932289124,"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/T12072","display_name":"Machine Learning and Algorithms","score":0.9984999895095825,"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/regret","display_name":"Regret","score":0.8021921515464783},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.7148652076721191},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.6252894997596741},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5292426943778992},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5290255546569824},{"id":"https://openalex.org/keywords/sample","display_name":"Sample (material)","score":0.5077065229415894},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.49501127004623413},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.4467080235481262},{"id":"https://openalex.org/keywords/online-learning","display_name":"Online learning","score":0.4456956386566162},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.44314736127853394},{"id":"https://openalex.org/keywords/stochastic-optimization","display_name":"Stochastic optimization","score":0.43595218658447266},{"id":"https://openalex.org/keywords/stochastic-approximation","display_name":"Stochastic approximation","score":0.4238669276237488},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.39011090993881226},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.33212780952453613},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.30374351143836975},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.22974157333374023}],"concepts":[{"id":"https://openalex.org/C50817715","wikidata":"https://www.wikidata.org/wiki/Q79895177","display_name":"Regret","level":2,"score":0.8021921515464783},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7148652076721191},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.6252894997596741},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5292426943778992},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5290255546569824},{"id":"https://openalex.org/C198531522","wikidata":"https://www.wikidata.org/wiki/Q485146","display_name":"Sample (material)","level":2,"score":0.5077065229415894},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.49501127004623413},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4467080235481262},{"id":"https://openalex.org/C2986087404","wikidata":"https://www.wikidata.org/wiki/Q15946010","display_name":"Online learning","level":2,"score":0.4456956386566162},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.44314736127853394},{"id":"https://openalex.org/C194387892","wikidata":"https://www.wikidata.org/wiki/Q1747770","display_name":"Stochastic optimization","level":2,"score":0.43595218658447266},{"id":"https://openalex.org/C55479107","wikidata":"https://www.wikidata.org/wiki/Q97663916","display_name":"Stochastic approximation","level":3,"score":0.4238669276237488},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.39011090993881226},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.33212780952453613},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.30374351143836975},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.22974157333374023},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C136764020","wikidata":"https://www.wikidata.org/wiki/Q466","display_name":"World Wide Web","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C43617362","wikidata":"https://www.wikidata.org/wiki/Q170050","display_name":"Chromatography","level":1,"score":0.0},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.0},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/3-540-44581-1_5","is_oa":false,"landing_page_url":"https://doi.org/10.1007/3-540-44581-1_5","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W1485026097","https://openalex.org/W1544068237","https://openalex.org/W1563088657","https://openalex.org/W1709057194","https://openalex.org/W1968444040","https://openalex.org/W2011395874","https://openalex.org/W2069317438","https://openalex.org/W2077008409","https://openalex.org/W2122789612","https://openalex.org/W2138263042","https://openalex.org/W2148603752","https://openalex.org/W2156909104","https://openalex.org/W2408196097","https://openalex.org/W2795056610","https://openalex.org/W3106701453","https://openalex.org/W6786454117","https://openalex.org/W7071374342"],"related_works":["https://openalex.org/W3041944716","https://openalex.org/W2124181538","https://openalex.org/W3207830353","https://openalex.org/W4286899070","https://openalex.org/W4323366756","https://openalex.org/W2734989445","https://openalex.org/W2403770454","https://openalex.org/W4285259204","https://openalex.org/W3012647659","https://openalex.org/W2118205332"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2025-10-10T00:00:00"}