{"id":"https://openalex.org/W7214905250","doi":"https://doi.org/10.48550/arxiv.2609.36033","title":"Dual-Anchor Acceleration Is Near-Optimal for Stochastic Monotone Root-Finding","display_name":"Dual-Anchor Acceleration Is Near-Optimal for Stochastic Monotone Root-Finding","publication_year":2026,"publication_date":"2026-09-28","ids":{"openalex":"https://openalex.org/W7214905250","doi":"https://doi.org/10.48550/arxiv.2609.36033"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.36033","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.36033","pdf_url":"https://arxiv.org/pdf/2609.36033","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","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.36033","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5115902718","display_name":"TaeHo Yoon","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I145311948","display_name":"Johns Hopkins University","ror":"https://ror.org/00za53h95","country_code":"US","type":"education","lineage":["https://openalex.org/I145311948"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Yoon, TaeHo","raw_affiliation_strings":["Department of Applied Mathematics and Statistics & Mathematical Institute for Data Science , Johns Hopkins Uni- versity"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics and Statistics & Mathematical Institute for Data Science , Johns Hopkins Uni- versity","institution_ids":["https://openalex.org/I145311948"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5075390126","display_name":"Nicolas Loizou","orcid":"https://orcid.org/0000-0003-4359-6492","observed_orcids":["https://orcid.org/0000-0003-4359-6492"]},"institutions":[{"id":"https://openalex.org/I145311948","display_name":"Johns Hopkins University","ror":"https://ror.org/00za53h95","country_code":"US","type":"education","lineage":["https://openalex.org/I145311948"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Loizou, Nicolas","raw_affiliation_strings":["Department of Applied Mathematics and Statistics & Mathematical Institute for Data Science , Johns Hopkins Uni- versity"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics and Statistics & Mathematical Institute for Data Science , Johns Hopkins Uni- versity","institution_ids":["https://openalex.org/I145311948"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I145311948"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.6273999810218811,"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":0.6273999810218811,"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/T10545","display_name":"Optimization and Variational Analysis","score":0.30959999561309814,"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"}},{"id":"https://openalex.org/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.007499999832361937,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/fixed-point-problems","display_name":"fixed point problems","score":0.8100000023841858},{"id":"https://openalex.org/keywords/variance-control","display_name":"variance control","score":0.9210000038146973},{"id":"https://openalex.org/keywords/oracle-complexity","display_name":"oracle complexity","score":0.8930000066757202},{"id":"https://openalex.org/keywords/monotone-operators","display_name":"monotone operators","score":0.6610000133514404},{"id":"https://openalex.org/keywords/stochastic-optimization","display_name":"stochastic optimization","score":0.4909999966621399}],"concepts":[{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.8011000156402588},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7028999924659729},{"id":"https://openalex.org/C55166926","wikidata":"https://www.wikidata.org/wiki/Q2892946","display_name":"Oracle","level":2,"score":0.6480000019073486},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5910000205039978},{"id":"https://openalex.org/C196267783","wikidata":"https://www.wikidata.org/wiki/Q4392490","display_name":"Resolvent","level":2,"score":0.5745999813079834},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4884999990463257},{"id":"https://openalex.org/C196083921","wikidata":"https://www.wikidata.org/wiki/Q7915758","display_name":"Variance (accounting)","level":2,"score":0.4668000042438507},{"id":"https://openalex.org/C117896860","wikidata":"https://www.wikidata.org/wiki/Q11376","display_name":"Acceleration","level":2,"score":0.46309998631477356},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.43470001220703125},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.4284000098705292},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.41909998655319214},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.4004000127315521},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.37059998512268066},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.34200000762939453},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.3165999948978424},{"id":"https://openalex.org/C198531522","wikidata":"https://www.wikidata.org/wiki/Q485146","display_name":"Sample (material)","level":2,"score":0.30070000886917114},{"id":"https://openalex.org/C55479107","wikidata":"https://www.wikidata.org/wiki/Q97663916","display_name":"Stochastic approximation","level":3,"score":0.29739999771118164},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.29429998993873596},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.29120001196861267},{"id":"https://openalex.org/C90377204","wikidata":"https://www.wikidata.org/wiki/Q1052594","display_name":"Uniform boundedness","level":3,"score":0.28630000352859497},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.2791999876499176},{"id":"https://openalex.org/C32645036","wikidata":"https://www.wikidata.org/wiki/Q475164","display_name":"Stochastic ordering","level":2,"score":0.2700999975204468},{"id":"https://openalex.org/C127491075","wikidata":"https://www.wikidata.org/wiki/Q7617825","display_name":"Stochastic modelling","level":2,"score":0.25760000944137573},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.25220000743865967}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.36033","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.36033","pdf_url":"https://arxiv.org/pdf/2609.36033","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.2609.36033","doi":"https://doi.org/10.48550/arxiv.2609.36033","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.36033","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.36033","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.36033","pdf_url":"https://arxiv.org/pdf/2609.36033","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":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G2169253178","display_name":"Collaborative Research: CIF: Medium: Post-Modern Min-Max Optimization Theory: Departure from Classical Minimization Theory","funder_award_id":"2504626","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214905250.pdf","grobid_xml":"https://content.openalex.org/works/W7214905250.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7202358158","https://openalex.org/W7214791645","https://openalex.org/W7216197545","https://openalex.org/W4417128709","https://openalex.org/W4395064890","https://openalex.org/W7212117869","https://openalex.org/W2138826651","https://openalex.org/W7214279250","https://openalex.org/W7162424641","https://openalex.org/W2534118885"],"abstract_inverted_index":{"Among":[0],"distinct":[1],"optimal":[2],"acceleration":[3],"mechanisms":[4],"for":[5],"deterministic":[6],"monotone":[7,102],"root-finding":[8],"problems":[9],"and":[10,49,85,103,139],"fixed-point":[11],"problems,":[12],"dual-anchoring":[13,38,80],"has":[14,40],"recently":[15],"been":[16],"shown":[17],"to":[18,60,145,170],"admit":[19],"a":[20,58,109,114,146],"more":[21],"robust":[22],"direct":[23],"stochastic":[24,37,82,91],"extension":[25],"than":[26],"standard":[27],"anchor":[28],"acceleration.":[29],"However,":[30],"without":[31],"additional":[32],"strong":[33],"monotonicity,":[34],"the":[35,61,142,151,157,165],"existing":[36],"guarantee":[39],"two":[41],"limitations:":[42],"first,":[43],"it":[44,51],"requires":[45],"cocoercivity":[46],"in":[47,156],"expectation,":[48],"second,":[50],"attains":[52],"only":[53],"$O(\u03b5^{-3})$":[54],"oracle":[55,116,154],"complexity,":[56],"leaving":[57],"gap":[59],"near-optimal":[62,115],"$\\tilde{O}(\u03b5^{-2})$":[63],"complexity":[64,117,155],"achieved":[65],"by":[66,78,96],"other":[67],"methods.":[68],"In":[69],"this":[70],"work,":[71],"we":[72],"address":[73],"both":[74],"of":[75,118],"these":[76,161],"limitations":[77],"combining":[79],"with":[81,93,111,113],"resolvent":[83],"approximation":[84],"optimized":[86],"variance":[87,94],"control.":[88],"For":[89],"unbiased":[90],"oracles":[92],"bounded":[95],"$\u03c3^2$,":[97],"where":[98,130],"sample":[99],"operators":[100],"are":[101],"uniformly":[104],"$L$-Lipschitz,":[105],"our":[106],"algorithm":[107],"finds":[108],"point":[110],"$\u03b5$-residual":[112],"$O":[119],"(":[120],"(LD":[121],"/":[122,127,137],"\u03b5)":[123],"\\ell":[124],"+":[125,135],"(\u03c3^2":[126],"\u03b5^2)":[128],"\\ell^2)$,":[129],"$\\ell":[131],"=":[132],"\\log":[133],"(1":[134],"LD":[136],"\u03b5)$":[138],"$D$":[140],"is":[141],"initial":[143],"distance":[144],"solution.":[147],"This":[148],"result":[149],"improves":[150],"best":[152],"known":[153],"noise-dominated":[158],"regime":[159],"under":[160],"samplewise":[162],"assumptions,":[163],"reducing":[164],"poly-logarithmic":[166],"factor":[167],"from":[168],"cubic":[169],"quadratic.":[171]},"counts_by_year":[],"updated_date":"2026-11-06T12:05:46.655746","created_date":"2026-10-01T00:00:00"}
