{"id":"https://openalex.org/W2271982975","doi":null,"title":"Second Order Stochastic Optimization in Linear Time.","display_name":"Second Order Stochastic Optimization in Linear Time.","publication_year":2016,"publication_date":"2016-02-12","ids":{"openalex":"https://openalex.org/W2271982975","mag":"2271982975"},"language":"en","primary_location":{"id":"mag:2271982975","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1602.03943","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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},"volume":null,"type":"preprint","indexed_in":[],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1602.03943","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5007875487","display_name":"Naman Agarwal","orcid":"https://orcid.org/0000-0003-0320-0238","observed_orcids":["https://orcid.org/0000-0003-0320-0238"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Naman Agarwal","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0003-0320-0238","affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5048046167","display_name":"Brian Bullins","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Brian Bullins","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5024431603","display_name":"Elad Hazan","orcid":"https://orcid.org/0000-0002-1566-3216","observed_orcids":["https://orcid.org/0000-0002-1566-3216"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Elad Hazan","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-1566-3216","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":40,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.0,"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"}},{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.0,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/linear-convergence","display_name":"linear convergence","score":0.5960000157356262},{"id":"https://openalex.org/keywords/hessian-approximation","display_name":"Hessian approximation","score":0.5960000157356262},{"id":"https://openalex.org/keywords/self-concordant-functions","display_name":"self-concordant functions","score":0.9470000267028809},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"convex optimization","score":0.781000018119812}],"concepts":[{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.643860399723053},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6122949719429016},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5982363224029541},{"id":"https://openalex.org/C194387892","wikidata":"https://www.wikidata.org/wiki/Q1747770","display_name":"Stochastic optimization","level":2,"score":0.5848770141601562},{"id":"https://openalex.org/C206688291","wikidata":"https://www.wikidata.org/wiki/Q7617819","display_name":"Stochastic gradient descent","level":3,"score":0.5637903213500977},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.431968629360199},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.42276039719581604},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.42219310998916626},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3519742488861084},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.3433692753314972},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.330752968788147},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.17532342672348022},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.08641317486763},{"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},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","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}],"mesh":[],"locations_count":1,"locations":[{"id":"mag:2271982975","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1602.03943","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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}],"best_oa_location":{"id":"mag:2271982975","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1602.03943","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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},"sustainable_development_goals":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W196761320","https://openalex.org/W1491622225","https://openalex.org/W1991083751","https://openalex.org/W2056641273","https://openalex.org/W2078409719","https://openalex.org/W2098741260","https://openalex.org/W2125993116","https://openalex.org/W2146502635","https://openalex.org/W2952215077","https://openalex.org/W3120740533"],"related_works":["https://openalex.org/W2006903949","https://openalex.org/W2597603852","https://openalex.org/W2146502635","https://openalex.org/W2112796928","https://openalex.org/W2107438106","https://openalex.org/W196761320","https://openalex.org/W3173030687","https://openalex.org/W3137079232","https://openalex.org/W3181247765","https://openalex.org/W2942536919","https://openalex.org/W3165523929","https://openalex.org/W2079901371","https://openalex.org/W3105169789","https://openalex.org/W2737743075","https://openalex.org/W2901718886","https://openalex.org/W2963415882","https://openalex.org/W2150102617","https://openalex.org/W2061570747","https://openalex.org/W1994616650","https://openalex.org/W1991083751"],"abstract_inverted_index":{"Stochastic":[0],"optimization":[1,57],"and,":[2],"in":[3,60],"particular,":[4],"first-order":[5],"stochastic":[6,54],"methods":[7],"are":[8],"a":[9,52,98],"cornerstone":[10],"of":[11,42,74,82,91,109],"modern":[12],"machine":[13,61],"learning":[14,62],"due":[15,37],"to":[16,27,38],"their":[17],"extremely":[18],"efficient":[19],"per-iteration":[20,30,72],"computational":[21],"cost.":[22],"Second-order":[23],"methods,":[24],"while":[25],"able":[26],"provide":[28],"faster":[29],"convergence,":[31],"have":[32],"been":[33],"much":[34],"less":[35],"explored":[36],"the":[39,44,71,79,88,110],"high":[40],"cost":[41,73],"computing":[43],"second-order":[45,53,83],"information.":[46],"In":[47],"this":[48],"paper":[49],"we":[50,95],"develop":[51],"method":[55,101],"for":[56,117],"problems":[58],"arising":[59],"based":[63],"on":[64],"novel":[65],"matrix":[66],"randomization":[67],"techniques":[68],"that":[69,97],"match":[70],"gradient":[75],"descent,":[76],"yet":[77],"enjoy":[78],"linear-convergence":[80],"properties":[81],"optimization.":[84],"We":[85,113],"also":[86],"consider":[87],"special":[89],"case":[90],"self-concordant":[92],"functions":[93],"where":[94],"show":[96],"first":[99],"order":[100],"can":[102],"achieve":[103],"linear":[104,119],"convergence":[105],"with":[106],"guarantees":[107],"independent":[108],"condition":[111],"number.":[112],"demonstrate":[114],"significant":[115],"speedups":[116],"training":[118],"classifiers":[120],"over":[121],"several":[122],"convex":[123],"benchmarks.":[124]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":8},{"year":2020,"cited_by_count":8},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2}],"updated_date":"2026-10-16T09:59:22.235173","created_date":"2025-10-10T00:00:00"}
