{"id":"https://openalex.org/W7140130810","doi":"https://doi.org/10.48550/arxiv.2603.19648","title":"Heavy-Tailed and Long-Range Dependent Noise in Stochastic Approximation: A Finite-Time Analysis","display_name":"Heavy-Tailed and Long-Range Dependent Noise in Stochastic Approximation: A Finite-Time Analysis","publication_year":2026,"publication_date":"2026-03-20","ids":{"openalex":"https://openalex.org/W7140130810","doi":"https://doi.org/10.48550/arxiv.2603.19648"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2603.19648","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.19648","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.2603.19648","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5130353182","display_name":"Siddharth Chandak","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chandak, Siddharth","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5130405589","display_name":"Anuj Yadav","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yadav, Anuj","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5130403649","display_name":"Ayfer Ozgur","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ozgur, Ayfer","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5002056995","display_name":"Nicholas Bambos","orcid":"https://orcid.org/0000-0001-9250-4553"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Bambos, Nicholas","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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9212999939918518,"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":0.9212999939918518,"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/T10462","display_name":"Reinforcement Learning in Robotics","score":0.013700000010430813,"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":0.009100000374019146,"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/martingale","display_name":"Martingale (probability theory)","score":0.5910000205039978},{"id":"https://openalex.org/keywords/noise","display_name":"Noise (video)","score":0.5422000288963318},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5110999941825867},{"id":"https://openalex.org/keywords/stochastic-gradient-descent","display_name":"Stochastic gradient descent","score":0.4742000102996826},{"id":"https://openalex.org/keywords/markov-chain","display_name":"Markov chain","score":0.444599986076355},{"id":"https://openalex.org/keywords/markov-process","display_name":"Markov process","score":0.4309000074863434},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.42260000109672546},{"id":"https://openalex.org/keywords/white-noise","display_name":"White noise","score":0.39079999923706055},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.3894999921321869}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5985000133514404},{"id":"https://openalex.org/C48406656","wikidata":"https://www.wikidata.org/wiki/Q534112","display_name":"Martingale (probability theory)","level":2,"score":0.5910000205039978},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5620999932289124},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.5422000288963318},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5110999941825867},{"id":"https://openalex.org/C206688291","wikidata":"https://www.wikidata.org/wiki/Q7617819","display_name":"Stochastic gradient descent","level":3,"score":0.4742000102996826},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.444599986076355},{"id":"https://openalex.org/C159886148","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov process","level":2,"score":0.4309000074863434},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.42260000109672546},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4090000092983246},{"id":"https://openalex.org/C112633086","wikidata":"https://www.wikidata.org/wiki/Q381287","display_name":"White noise","level":2,"score":0.39079999923706055},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.3894999921321869},{"id":"https://openalex.org/C55479107","wikidata":"https://www.wikidata.org/wiki/Q97663916","display_name":"Stochastic approximation","level":3,"score":0.3788999915122986},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.37619999051094055},{"id":"https://openalex.org/C179254644","wikidata":"https://www.wikidata.org/wiki/Q13222844","display_name":"Moment (physics)","level":2,"score":0.3750999867916107},{"id":"https://openalex.org/C97541855","wikidata":"https://www.wikidata.org/wiki/Q830687","display_name":"Reinforcement learning","level":2,"score":0.35269999504089355},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.34860000014305115},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3400000035762787},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.33009999990463257},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.3249000012874603},{"id":"https://openalex.org/C29265498","wikidata":"https://www.wikidata.org/wiki/Q7047719","display_name":"Noise measurement","level":3,"score":0.2978000044822693},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2948000133037567},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.2930000126361847},{"id":"https://openalex.org/C2986577269","wikidata":"https://www.wikidata.org/wiki/Q11306265","display_name":"Random noise","level":2,"score":0.2669999897480011},{"id":"https://openalex.org/C114996537","wikidata":"https://www.wikidata.org/wiki/Q4854529","display_name":"Colors of noise","level":3,"score":0.26489999890327454},{"id":"https://openalex.org/C58435881","wikidata":"https://www.wikidata.org/wiki/Q1868500","display_name":"Local martingale","level":3,"score":0.2606000006198883},{"id":"https://openalex.org/C200378446","wikidata":"https://www.wikidata.org/wiki/Q4147391","display_name":"Gradient noise","level":5,"score":0.25220000743865967},{"id":"https://openalex.org/C163294075","wikidata":"https://www.wikidata.org/wiki/Q581861","display_name":"Noise reduction","level":2,"score":0.25200000405311584}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2603.19648","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.19648","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.2603.19648","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.19648","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":{"Stochastic":[0],"approximation":[1],"(SA)":[2],"is":[3],"a":[4,57,93],"fundamental":[5],"iterative":[6],"framework":[7,111],"with":[8,26],"broad":[9],"applications":[10],"in":[11,73],"reinforcement":[12],"learning":[13],"and":[14,36,41,87,117,120],"optimization.":[15],"Classical":[16],"analyses":[17],"typically":[18],"rely":[19],"on":[20],"martingale":[21],"difference":[22],"or":[23],"Markov":[24],"noise":[25,64,101],"bounded":[27],"second":[28],"moments,":[29],"but":[30],"many":[31],"practical":[32],"settings,":[33,75],"including":[34],"finance":[35],"communications,":[37],"frequently":[38],"encounter":[39],"heavy-tailed":[40],"long-range":[42],"dependent":[43],"(LRD)":[44],"noise.":[45],"In":[46],"this":[47],"work,":[48],"we":[49,107],"study":[50],"SA":[51],"for":[52],"finding":[53],"the":[54,68,82,98,104],"root":[55],"of":[56,84,100],"strongly":[58],"monotone":[59],"operator":[60],"under":[61],"these":[62],"non-classical":[63],"models.":[65],"We":[66],"establish":[67],"first":[69],"finite-time":[70,123],"moment":[71],"bounds":[72],"both":[74],"providing":[76],"explicit":[77],"convergence":[78],"rates":[79],"that":[80,96],"quantify":[81],"impact":[83,99],"heavy":[85],"tails":[86],"temporal":[88],"dependence.":[89],"Our":[90],"analysis":[91,124],"employs":[92],"noise-averaging":[94],"argument":[95],"regularizes":[97],"without":[102],"modifying":[103],"iteration.":[105],"Finally,":[106],"apply":[108],"our":[109,122],"general":[110],"to":[112],"stochastic":[113],"gradient":[114,118],"descent":[115],"(SGD)":[116],"play,":[119],"corroborate":[121],"through":[125],"numerical":[126],"experiments.":[127]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-03-24T00:00:00"}
