{"id":"https://openalex.org/W2885288625","doi":"https://doi.org/10.5075/epfl-thesis-8765","title":"Learning without Smoothness and Strong Convexity","display_name":"Learning without Smoothness and Strong Convexity","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2885288625","doi":"https://doi.org/10.5075/epfl-thesis-8765","mag":"2885288625"},"language":"en","primary_location":{"id":"pmh:oai:infoscience.epfl.ch:255948","is_oa":true,"landing_page_url":"https://infoscience.epfl.ch/handle/20.500.14299/147203","pdf_url":"http://infoscience.epfl.ch/record/255948","source":{"id":"https://openalex.org/S4306400487","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":"doctoral thesis"},"type":"article","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://infoscience.epfl.ch/record/255948","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5089741364","display_name":"Yen-Huan Li","orcid":"https://orcid.org/0000-0003-2454-7249"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Li, Yen-Huan","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5089741364"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"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/T12072","display_name":"Machine Learning and Algorithms","score":0.9761999845504761,"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/T12072","display_name":"Machine Learning and Algorithms","score":0.9761999845504761,"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/convexity","display_name":"Convexity","score":0.6923002004623413},{"id":"https://openalex.org/keywords/smoothness","display_name":"Smoothness","score":0.6828726530075073},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.42051663994789124},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.41830819845199585},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3949855864048004},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.24703660607337952},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2070641815662384}],"concepts":[{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.6923002004623413},{"id":"https://openalex.org/C102634674","wikidata":"https://www.wikidata.org/wiki/Q868473","display_name":"Smoothness","level":2,"score":0.6828726530075073},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.42051663994789124},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.41830819845199585},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3949855864048004},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.24703660607337952},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2070641815662384},{"id":"https://openalex.org/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"pmh:oai:infoscience.epfl.ch:255948","is_oa":true,"landing_page_url":"https://infoscience.epfl.ch/handle/20.500.14299/147203","pdf_url":"http://infoscience.epfl.ch/record/255948","source":{"id":"https://openalex.org/S4306400487","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":"doctoral thesis"},{"id":"doi:10.5075/epfl-thesis-8765","is_oa":true,"landing_page_url":"https://doi.org/10.5075/epfl-thesis-8765","pdf_url":null,"source":{"id":"https://openalex.org/S4306400488","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":"thesis"},{"id":"mag:2885288625","is_oa":false,"landing_page_url":"https://infoscience.epfl.ch/record/255948","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":null}],"best_oa_location":{"id":"pmh:oai:infoscience.epfl.ch:255948","is_oa":true,"landing_page_url":"https://infoscience.epfl.ch/handle/20.500.14299/147203","pdf_url":"http://infoscience.epfl.ch/record/255948","source":{"id":"https://openalex.org/S4306400487","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":"doctoral thesis"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","score":0.46000000834465027,"display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2885288625.pdf"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2344964557","https://openalex.org/W2962955878","https://openalex.org/W2040657720","https://openalex.org/W1411365503","https://openalex.org/W2109125555","https://openalex.org/W2511890448","https://openalex.org/W3099748020","https://openalex.org/W2963217995","https://openalex.org/W2416874002","https://openalex.org/W2141044033","https://openalex.org/W2905865189","https://openalex.org/W2472968238","https://openalex.org/W2558784134","https://openalex.org/W2027051720","https://openalex.org/W1967474871","https://openalex.org/W2819981554","https://openalex.org/W1605636162","https://openalex.org/W2620850570","https://openalex.org/W1609944796","https://openalex.org/W1985298333"],"abstract_inverted_index":{"Recent":[0],"advances":[1],"in":[2,33,188,267],"statistical":[3,251],"learning":[4,252],"and":[5,20,37,76,115,157,206,254],"convex":[6,102],"optimization":[7,103,133],"have":[8],"inspired":[9],"many":[10],"successful":[11],"practices.":[12],"Standard":[13],"theories":[14],"assume":[15],"smoothness---bounded":[16],"gradient,":[17],"Hessian,":[18],"etc.---":[19],"strong":[21,158],"convexity":[22,159],"of":[23,169,226],"the":[24,41,62,67,126,150,162,167,202,211,227,231,262],"loss":[25,70,122,164],"function.":[26],"Unfortunately,":[27],"such":[28,111],"conditions":[29,42],"may":[30],"not":[31,137,265],"hold":[32],"important":[34],"real-world":[35],"applications,":[36],"sometimes,":[38],"to":[39,93,121,190,201,220,236],"fulfill":[40],"incurs":[43],"unnecessary":[44],"performance":[45,186],"degradation.":[46],"Below":[47],"are":[48,90],"three":[49,203],"examples.":[50],"1.":[51],"The":[52,98,140,176],"standard":[53,99,141],"theory":[54,100,142],"for":[55,78,101,132,143,242],"variable":[56],"selection":[57,114],"via":[58,172],"L_1-penalization":[59],"only":[60],"considers":[61,104],"linear":[63],"regression":[64,88],"model,":[65],"as":[66,112,249],"corresponding":[68],"quadratic":[69,163],"function":[71],"has":[72],"a":[73,238,250],"constant":[74],"Hessian":[75],"allows":[77],"exact":[79],"second-order":[80],"Taylor":[81],"series":[82],"expansion.":[83],"In":[84,194],"practice,":[85],"however,":[86,119,181],"non-linear":[87],"models":[89],"often":[91],"chosen":[92],"match":[94],"data":[95],"characteristics.":[96],"2.":[97],"almost":[105],"exclusively":[106],"smooth":[107],"functions.":[108],"Important":[109],"applications":[110],"portfolio":[113],"quantum":[116],"state":[117],"estimation,":[118],"correspond":[120],"functions":[123],"that":[124],"violate":[125],"smoothness":[127,156,228],"assumption;":[128],"existing":[129],"convergence":[130],"guarantees":[131,149],"algorithms":[134],"hence":[135],"do":[136],"apply.":[138],"3.":[139],"compressive":[144,243,247],"magnetic":[145],"resonance":[146],"imaging":[147],"(MRI)":[148],"restricted":[151,165],"isometry":[152],"property":[153],"(RIP)":[154],"---a":[155],"condition":[160],"on":[161,166],"set":[168],"sparse":[170],"vectors---":[171],"random":[173,177],"uniform":[174,178],"sampling.":[175],"sampling":[179,192],"strategy,":[180],"yields":[182],"unsatisfactory":[183],"signal":[184],"reconstruction":[185],"empirically,":[187],"comparison":[189],"heuristic":[191],"approaches.":[193],"this":[195,268],"thesis,":[196],"we":[197],"provide":[198],"rigorous":[199],"solutions":[200],"examples":[204],"above":[205],"other":[207],"related":[208],"problems.":[209],"For":[210,230],"first":[212],"two":[213],"problems":[214],"above,":[215],"our":[216,233],"key":[217],"idea":[218],"is":[219,235,264],"instead":[221],"consider":[222],"weaker":[223],"localized":[224],"versions":[225],"condition.":[229],"third,":[232],"solution":[234],"propose":[237],"new":[239],"theoretical":[240],"framework":[241],"MRI:":[244],"We":[245],"pose":[246],"MRI":[248],"problem,":[253],"solve":[255],"it":[256],"by":[257],"empirical":[258],"risk":[259],"minimization.":[260],"Interestingly,":[261],"RIP":[263],"required":[266],"framework.":[269]},"counts_by_year":[],"updated_date":"2025-11-06T06:51:31.235846","created_date":"2025-10-10T00:00:00"}