{"id":"https://openalex.org/W7213225151","doi":"https://doi.org/10.48550/arxiv.2609.13646","title":"Curvature-Independent Regret Bounds for Distributed Online Optimization on Hadamard Manifolds","display_name":"Curvature-Independent Regret Bounds for Distributed Online Optimization on Hadamard Manifolds","publication_year":2026,"publication_date":"2026-09-12","ids":{"openalex":"https://openalex.org/W7213225151","doi":"https://doi.org/10.48550/arxiv.2609.13646"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.13646","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.13646","pdf_url":"https://arxiv.org/pdf/2609.13646","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/2609.13646","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5110966332","display_name":"Zhanyuan Cai","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I12912129","display_name":"Northeastern University","ror":"https://ror.org/04t5xt781","country_code":"US","type":"education","lineage":["https://openalex.org/I12912129"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Cai, Zhanyuan","raw_affiliation_strings":["Department of Mechan- ical and Industrial Engineering , Northeastern Univer- sity , Boston , MA 02115 "],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mechan- ical and Industrial Engineering , Northeastern Univer- sity , Boston , MA 02115 ","institution_ids":["https://openalex.org/I12912129"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5099038760","display_name":"Emre Sahinoglu","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I12912129","display_name":"Northeastern University","ror":"https://ror.org/04t5xt781","country_code":"US","type":"education","lineage":["https://openalex.org/I12912129"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Sahinoglu, Emre","raw_affiliation_strings":["Department of Mechan- ical and Industrial Engineering , Northeastern Univer- sity , Boston , MA 02115 "],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mechan- ical and Industrial Engineering , Northeastern Univer- sity , Boston , MA 02115 ","institution_ids":["https://openalex.org/I12912129"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5040922600","display_name":"Shahin Shahrampour","orcid":"https://orcid.org/0000-0003-3093-8510","observed_orcids":["https://orcid.org/0000-0003-3093-8510"]},"institutions":[{"id":"https://openalex.org/I12912129","display_name":"Northeastern University","ror":"https://ror.org/04t5xt781","country_code":"US","type":"education","lineage":["https://openalex.org/I12912129"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Shahrampour, Shahin","raw_affiliation_strings":["Department of Mechan- ical and Industrial Engineering , Northeastern Univer- sity , Boston , MA 02115 "],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mechan- ical and Industrial Engineering , Northeastern Univer- sity , Boston , MA 02115 ","institution_ids":["https://openalex.org/I12912129"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I12912129"],"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/T10249","display_name":"Distributed Control Multi-Agent Systems","score":0.461899995803833,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"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":0.461899995803833,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.1420000046491623,"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/T12101","display_name":"Advanced Bandit Algorithms Research","score":0.12720000743865967,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/distributed-online-optimization","display_name":"distributed online optimization","score":0.8230000138282776},{"id":"https://openalex.org/keywords/riemannian-optimization","display_name":"Riemannian optimization","score":0.9309999942779541},{"id":"https://openalex.org/keywords/hadamard-manifolds","display_name":"Hadamard manifolds","score":0.9990000128746033},{"id":"https://openalex.org/keywords/regret-bounds","display_name":"regret bounds","score":0.8270000219345093},{"id":"https://openalex.org/keywords/spectral-gap","display_name":"spectral gap","score":0.7379999756813049},{"id":"https://openalex.org/keywords/hyperbolic-embeddings","display_name":"hyperbolic embeddings","score":0.8899999856948853},{"id":"https://openalex.org/keywords/distributed-optimization","display_name":"distributed optimization","score":0.49300000071525574}],"concepts":[{"id":"https://openalex.org/C165818556","wikidata":"https://www.wikidata.org/wiki/Q213488","display_name":"Geodesic","level":2,"score":0.6865000128746033},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6791999936103821},{"id":"https://openalex.org/C42448751","wikidata":"https://www.wikidata.org/wiki/Q855622","display_name":"Sectional curvature","level":4,"score":0.614300012588501},{"id":"https://openalex.org/C60292330","wikidata":"https://www.wikidata.org/wiki/Q1014065","display_name":"Hadamard transform","level":2,"score":0.5209000110626221},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.4925999939441681},{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.49140000343322754},{"id":"https://openalex.org/C12089564","wikidata":"https://www.wikidata.org/wiki/Q1195879","display_name":"Ricci curvature","level":3,"score":0.45489999651908875},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4487000107765198},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.448199987411499},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.4374000132083893},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.42089998722076416},{"id":"https://openalex.org/C2779593128","wikidata":"https://www.wikidata.org/wiki/Q632814","display_name":"Riemannian manifold","level":2,"score":0.4205999970436096},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4154999852180481},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.3894999921321869},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.382999986410141},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.37049999833106995},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.3472999930381775},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3409000039100647},{"id":"https://openalex.org/C109546454","wikidata":"https://www.wikidata.org/wiki/Q3798604","display_name":"Information geometry","level":4,"score":0.334199994802475},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.3280999958515167},{"id":"https://openalex.org/C50817715","wikidata":"https://www.wikidata.org/wiki/Q79895177","display_name":"Regret","level":2,"score":0.3158999979496002},{"id":"https://openalex.org/C16140857","wikidata":"https://www.wikidata.org/wiki/Q945953","display_name":"Gaussian curvature","level":3,"score":0.3089999854564667},{"id":"https://openalex.org/C12520029","wikidata":"https://www.wikidata.org/wiki/Q1147161","display_name":"Scalar curvature","level":3,"score":0.2912999987602234},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.2806999981403351},{"id":"https://openalex.org/C196921405","wikidata":"https://www.wikidata.org/wiki/Q786431","display_name":"Online algorithm","level":2,"score":0.2782999873161316},{"id":"https://openalex.org/C117160843","wikidata":"https://www.wikidata.org/wiki/Q338652","display_name":"Sublinear function","level":2,"score":0.27810001373291016},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2777000069618225},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.26739999651908875},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.2653000056743622},{"id":"https://openalex.org/C14196021","wikidata":"https://www.wikidata.org/wiki/Q7240881","display_name":"Prescribed scalar curvature problem","level":5,"score":0.26440000534057617},{"id":"https://openalex.org/C102224218","wikidata":"https://www.wikidata.org/wiki/Q25344559","display_name":"Exponential map (Riemannian geometry)","level":5,"score":0.26260000467300415},{"id":"https://openalex.org/C83677898","wikidata":"https://www.wikidata.org/wiki/Q1878538","display_name":"Hyperbolic space","level":2,"score":0.2614000141620636},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.25600001215934753},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.25130000710487366}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.13646","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.13646","pdf_url":"https://arxiv.org/pdf/2609.13646","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.2609.13646","doi":"https://doi.org/10.48550/arxiv.2609.13646","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.13646","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:2609.13646","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.13646","pdf_url":"https://arxiv.org/pdf/2609.13646","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/G1440818829","display_name":"CAREER: Foundations of Scalable, Fast, and Online Decentralized Manifold Optimization in Multi-Agent Networks","funder_award_id":"2442321","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4524843571","display_name":"Collaborative Research: Consensus and Distributed Optimization in Non-Convex Environments with Applications to Networked Machine Learning","funder_award_id":"2240788","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6671297155","display_name":null,"funder_award_id":"CAREER","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"},{"id":"https://openalex.org/F4320337392","display_name":"Division of Electrical, Communications and Cyber Systems","ror":"https://ror.org/01krpsy48"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7213225151.pdf","grobid_xml":"https://content.openalex.org/works/W7213225151.grobid-xml"},"referenced_works_count":6,"referenced_works":["https://openalex.org/W2808084307","https://openalex.org/W4393212700","https://openalex.org/W4403324107","https://openalex.org/W4416068121","https://openalex.org/W4416453954","https://openalex.org/W7170141733"],"related_works":["https://openalex.org/W4416068121","https://openalex.org/W4417508356","https://openalex.org/W4403324107","https://openalex.org/W7170141733","https://openalex.org/W4407012381","https://openalex.org/W3174059757","https://openalex.org/W4224276255","https://openalex.org/W7139145284","https://openalex.org/W4409095533","https://openalex.org/W4416453954"],"abstract_inverted_index":{"This":[0],"work":[1,11],"addresses":[2],"decentralized":[3,130],"online":[4,131],"Riemannian":[5,46,69,77],"optimization":[6,22,132],"on":[7,30,133,137],"Hadamard":[8,134],"manifolds.":[9,135],"Prior":[10],"under":[12],"geodesic":[13],"convexity":[14],"(g-convexity)":[15],"may":[16,35],"require":[17],"curvature":[18,55],"information":[19],"in":[20],"the":[21,31,38,54,102,116,124,141],"analysis,":[23],"typically":[24],"through":[25],"a":[26,58],"finite":[27],"lower":[28],"bound":[29],"sectional":[32],"curvature.":[33,150],"Curvature":[34],"also":[36],"enter":[37],"step":[39],"size":[40],"or":[41],"contraction":[42],"factor":[43],"of":[44,61],"tangent-space":[45],"consensus":[47],"schemes.":[48],"In":[49],"this":[50],"work,":[51],"we":[52,92],"relax":[53],"dependence":[56,112],"for":[57,129],"narrower":[59],"class":[60],"horospherical":[62],"convex":[63],"(h-convex)":[64],"functions.":[65],"We":[66],"study":[67],"Distributed":[68],"Online":[70],"Gradient":[71],"Descent":[72],"(D-ROGD),":[73],"which":[74],"combines":[75],"local":[76,90],"h-subgradient":[78],"updates":[79],"with":[80,106,110,144],"an":[81],"implicit":[82],"Fr\u00e9chet-mean":[83],"consensus.":[84],"For":[85],"h-convex":[86,89],"and":[87,95],"strongly":[88],"objectives,":[91],"establish":[93],"$O(\\sqrt{T})$":[94],"$O(\\log":[96],"T)$":[97],"static":[98],"regret,":[99],"respectively,":[100],"matching":[101],"corresponding":[103],"Euclidean":[104],"rates":[105],"respect":[107],"to":[108,149],"$T$,":[109],"network":[111],"governed":[113],"solely":[114],"by":[115],"spectral":[117],"gap.":[118],"To":[119],"our":[120],"knowledge,":[121],"these":[122],"are":[123],"first":[125],"curvature-independent":[126],"regret":[127],"guarantees":[128],"Experiments":[136],"hyperbolic":[138],"embeddings":[139],"corroborate":[140],"predicted":[142],"rates,":[143],"no":[145],"observable":[146],"degradation":[147],"due":[148]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-16T00:00:00"}
