{"id":"https://openalex.org/W7164573562","doi":"https://doi.org/10.48550/arxiv.2606.12675","title":"A Communication Complexity Lower Bound for Nonuniformly Convex Consensus Optimization","display_name":"A Communication Complexity Lower Bound for Nonuniformly Convex Consensus Optimization","publication_year":2026,"publication_date":"2026-06-10","ids":{"openalex":"https://openalex.org/W7164573562","doi":"https://doi.org/10.48550/arxiv.2606.12675"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2606.12675","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.12675","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,"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"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2606.12675","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5138540943","display_name":"Demyan Yarmoshik","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yarmoshik, Demyan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5133605365","display_name":"Maxim Klimenko","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Klimenko, Maxim","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":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/T10249","display_name":"Distributed Control Multi-Agent Systems","score":0.48010000586509705,"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"}},"topics":[{"id":"https://openalex.org/T10249","display_name":"Distributed Control Multi-Agent Systems","score":0.48010000586509705,"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"}},{"id":"https://openalex.org/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.14509999752044678,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.06650000065565109,"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/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.6625999808311462},{"id":"https://openalex.org/keywords/communication-complexity","display_name":"Communication complexity","score":0.5957000255584717},{"id":"https://openalex.org/keywords/oracle","display_name":"Oracle","score":0.5644000172615051},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.5031999945640564},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.4767000079154968},{"id":"https://openalex.org/keywords/computational-complexity-theory","display_name":"Computational complexity theory","score":0.46470001339912415},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.46160000562667847},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.4156000018119812}],"concepts":[{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.6625999808311462},{"id":"https://openalex.org/C179145077","wikidata":"https://www.wikidata.org/wiki/Q5154130","display_name":"Communication complexity","level":2,"score":0.5957000255584717},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5812000036239624},{"id":"https://openalex.org/C55166926","wikidata":"https://www.wikidata.org/wiki/Q2892946","display_name":"Oracle","level":2,"score":0.5644000172615051},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.5031999945640564},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.4767000079154968},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.46470001339912415},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.46160000562667847},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.4156000018119812},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.40230000019073486},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.39070001244544983},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.3837999999523163},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.3718000054359436},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.36230000853538513},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.3504999876022339},{"id":"https://openalex.org/C2779145032","wikidata":"https://www.wikidata.org/wiki/Q191494","display_name":"Digraph","level":2,"score":0.3481999933719635},{"id":"https://openalex.org/C146380142","wikidata":"https://www.wikidata.org/wiki/Q1137726","display_name":"Directed graph","level":2,"score":0.3449999988079071},{"id":"https://openalex.org/C192126672","wikidata":"https://www.wikidata.org/wiki/Q1068715","display_name":"Telecommunications network","level":2,"score":0.33980000019073486},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.33719998598098755},{"id":"https://openalex.org/C2780897414","wikidata":"https://www.wikidata.org/wiki/Q7600592","display_name":"Star (game theory)","level":2,"score":0.30410000681877136},{"id":"https://openalex.org/C199845137","wikidata":"https://www.wikidata.org/wiki/Q145490","display_name":"Network topology","level":2,"score":0.2980000078678131},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.29190000891685486},{"id":"https://openalex.org/C2164484","wikidata":"https://www.wikidata.org/wiki/Q5170150","display_name":"Core (optical fiber)","level":2,"score":0.27149999141693115},{"id":"https://openalex.org/C130120984","wikidata":"https://www.wikidata.org/wiki/Q2835898","display_name":"Distributed algorithm","level":2,"score":0.2513999938964844}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2606.12675","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.12675","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,"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":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2606.12675","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.12675","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,"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"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0,62],"study":[1],"the":[2,22,34,51,79,83,90,94,105,121],"communication":[3,37,73],"complexity":[4,49,96],"of":[5,36,68,82,89,123],"convex":[6],"decentralized":[7],"optimization":[8],"over":[9],"time-varying":[10],"networks,":[11],"where":[12,75],"$n$":[13],"nodes":[14,57],"hold":[15],"private":[16],"functions":[17],"and":[18,86,126],"must":[19],"agree":[20],"on":[21,111],"global":[23,91],"minimizer":[24],"using":[25],"only":[26,59],"synchronous":[27],"exchanges":[28],"with":[29],"neighbors.":[30],"The":[31,108],"cost":[32],"is":[33,78],"number":[35,81],"rounds":[38],"to":[39,47,129],"reach":[40],"accuracy":[41],"$\\varepsilon$":[42],"--":[43],"a":[44,64],"measure":[45],"akin":[46],"round":[48,95],"in":[50,104],"LOCAL":[52],"model,":[53],"but":[54],"constrained":[55],"by":[56],"sharing":[58],"oracle":[60],"responses.":[61],"prove":[63],"new":[65],"lower":[66],"bound":[67],"$\u03a9\\!\\left(\u03c7_{\\mathcal":[69],"G}":[70],"\\sqrt{\u03ba_g}\\,\\log\\frac{n}{\u03c7_{\\mathcal":[71],"G}}\\log\\frac1\\varepsilon\\right)$":[72],"rounds,":[74],"$\u03c7_{\\mathcal":[76],"G}$":[77],"condition":[80],"network":[84],"Laplacians":[85],"$\u03ba_g$":[87],"that":[88],"objective,":[92],"showing":[93],"attainable":[97],"under":[98],"uniform":[99],"regularity":[100],"cannot":[101],"be":[102],"matched":[103],"nonuniform":[106],"regime.":[107],"construction":[109],"rests":[110],"spectral":[112,131],"graph":[113],"theory:":[114],"we":[115],"embed":[116],"time-rotating":[117],"star":[118],"gadgets":[119],"into":[120],"edges":[122],"an":[124],"expander":[125],"patch":[127],"them":[128],"preserve":[130],"connectivity.":[132]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-06-13T00:00:00"}