{"id":"https://openalex.org/W4392575863","doi":"https://doi.org/10.48550/arxiv.2403.03562","title":"Efficient Algorithms for Empirical Group Distributionally Robust Optimization and Beyond","display_name":"Efficient Algorithms for Empirical Group Distributionally Robust Optimization and Beyond","publication_year":2024,"publication_date":"2024-03-06","ids":{"openalex":"https://openalex.org/W4392575863","doi":"https://doi.org/10.48550/arxiv.2403.03562"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2403.03562","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2403.03562","pdf_url":"https://arxiv.org/pdf/2403.03562","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":null,"raw_type":"text"},"volume":null,"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2403.03562","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5109689425","display_name":"Dingzhi Yu","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yu, Dingzhi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5113397252","display_name":"Yunuo Cai","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Cai, Yunuo","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5072314928","display_name":"Wei Jiang","orcid":"https://orcid.org/0000-0003-0142-4465","observed_orcids":["https://orcid.org/0000-0003-0142-4465","https://orcid.org/0009-0009-7980-3626"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jiang, Wei","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5100448142","display_name":"Lijun Zhang","orcid":"https://orcid.org/0000-0001-5697-4611","observed_orcids":["https://orcid.org/0000-0001-5697-4611"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhang, Lijun","raw_affiliation_strings":[],"raw_orcid":null,"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":true,"cited_by_count":1,"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":0.9916999936103821,"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":0.9916999936103821,"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/T11413","display_name":"Risk and Portfolio Optimization","score":0.0019000000320374966,"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/T10249","display_name":"Distributed Control Multi-Agent Systems","score":0.0006000000284984708,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/empirical-risk-minimization","display_name":"empirical risk minimization","score":0.8090000152587891},{"id":"https://openalex.org/keywords/variance-reduction","display_name":"variance reduction","score":0.8859999775886536},{"id":"https://openalex.org/keywords/cluster-sampling","display_name":"cluster sampling","score":0.781000018119812},{"id":"https://openalex.org/keywords/lipschitz-constant","display_name":"Lipschitz constant","score":0.8289999961853027},{"id":"https://openalex.org/keywords/computational-complexity","display_name":"computational complexity","score":0.5059999823570251}],"concepts":[{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.6246933937072754},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5510684251785278},{"id":"https://openalex.org/C2987595161","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Optimization algorithm","level":2,"score":0.5090917944908142},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.47979384660720825},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.31596535444259644},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2447361946105957},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","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}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2403.03562","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2403.03562","pdf_url":"https://arxiv.org/pdf/2403.03562","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":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2403.03562","doi":"https://doi.org/10.48550/arxiv.2403.03562","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2403.03562","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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2403.03562","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2403.03562","pdf_url":"https://arxiv.org/pdf/2403.03562","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":null,"raw_type":"text"},"sustainable_development_goals":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G3388556471","display_name":null,"funder_award_id":"2022ZD0114801","funder_id":"https://openalex.org/F4320329860","funder_display_name":"National Science and Technology Major Project"},{"id":"https://openalex.org/G528746023","display_name":null,"funder_award_id":"61921006","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6521948476","display_name":null,"funder_award_id":"62122037","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320329860","display_name":"National Science and Technology Major Project","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4392575863.pdf","grobid_xml":"https://content.openalex.org/works/W4392575863.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W4366549320","https://openalex.org/W4287863136","https://openalex.org/W3006015132","https://openalex.org/W2965078190","https://openalex.org/W3040644038","https://openalex.org/W4311207076","https://openalex.org/W4313459248","https://openalex.org/W3203633096","https://openalex.org/W2355226480"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,74,139],"investigate":[4],"the":[5,18,70,83,116,128,151,170],"empirical":[6,20,28,152],"counterpart":[7],"of":[8,110,119,134,162,167,172],"Group":[9],"Distributionally":[10],"Robust":[11],"Optimization":[12,156],"(GDRO),":[13],"which":[14],"aims":[15],"to":[16,44,81,148],"minimize":[17],"maximal":[19],"risk":[21],"across":[22],"$m$":[23,122],"distinct":[24],"groups.":[25,98,123],"We":[26],"formulate":[27],"GDRO":[29],"as":[30],"a":[31,52,63,76,87,107,132,142],"$\\textit{two-level}$":[32],"finite-sum":[33,72],"convex-concave":[34],"minimax":[35],"optimization":[36,144],"problem":[37],"and":[38,91],"develop":[39,141],"an":[40],"algorithm":[41,56,145],"called":[42,146],"ALEG":[43,50,103],"benefit":[45],"from":[46],"its":[47],"special":[48],"structure.":[49],"is":[51,115],"double-looped":[53],"stochastic":[54,84],"primal-dual":[55],"that":[57,102,166],"incorporates":[58],"variance":[59,94],"reduction":[60,95],"techniques":[61],"into":[62],"modified":[64],"mirror":[65],"prox":[66],"routine.":[67],"To":[68],"exploit":[69],"two-level":[71],"structure,":[73],"propose":[75],"simple":[77],"group":[78],"sampling":[79],"strategy":[80],"construct":[82],"gradient":[85],"with":[86,150],"smaller":[88],"Lipschitz":[89],"constant":[90],"then":[92],"perform":[93],"for":[96],"all":[97],"Theoretical":[99],"analysis":[100],"shows":[101],"achieves":[104],"$\\varepsilon$-accuracy":[105],"within":[106],"computation":[108,160],"complexity":[109,161],"$\\mathcal{O}\\left(\\frac{m\\sqrt{\\bar{n}\\ln{m}}}{\\varepsilon}\\right)$,":[111],"where":[112],"$\\bar":[113],"n$":[114],"average":[117],"number":[118],"samples":[120],"among":[121],"Notably,":[124],"our":[125],"approach":[126],"outperforms":[127],"state-of-the-art":[129],"method":[130],"by":[131],"factor":[133],"$\\sqrt{m}$.":[135],"Based":[136],"on":[137],"ALEG,":[138,168],"further":[140],"two-stage":[143],"ALEM":[147,163],"deal":[149],"Minimax":[153],"Excess":[154],"Risk":[155],"(MERO)":[157],"problem.":[158],"The":[159],"nearly":[164],"matches":[165],"surpassing":[169],"rates":[171],"existing":[173],"methods.":[174]},"counts_by_year":[{"year":2024,"cited_by_count":1}],"updated_date":"2026-10-16T09:59:22.235173","created_date":"2024-03-08T00:00:00"}
