{"id":"https://openalex.org/W7204886889","doi":"https://doi.org/10.48550/arxiv.2608.30382","title":"Convergence rates for the RMSprop optimizer with full control of the hyperparameters","display_name":"Convergence rates for the RMSprop optimizer with full control of the hyperparameters","publication_year":2026,"publication_date":"2026-08-31","ids":{"openalex":"https://openalex.org/W7204886889","doi":"https://doi.org/10.48550/arxiv.2608.30382"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.30382","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.30382","pdf_url":"https://arxiv.org/pdf/2608.30382","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/2608.30382","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5086965787","display_name":"Steffen Dereich","orcid":"https://orcid.org/0000-0001-9591-9340","observed_orcids":["https://orcid.org/0000-0001-9591-9340"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Dereich, Steffen","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5074382323","display_name":"Arnulf Jentzen","orcid":"https://orcid.org/0000-0002-9840-3339","observed_orcids":["https://orcid.org/0000-0002-9840-3339"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jentzen, Arnulf","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":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":1.0,"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":1.0,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.0,"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"}},{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.0,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/rmsprop","display_name":"RMSProp","score":0.9459999799728394},{"id":"https://openalex.org/keywords/convergence-rate","display_name":"convergence rate","score":0.7960000038146973},{"id":"https://openalex.org/keywords/non-asymptotic-error-bounds","display_name":"non-asymptotic error bounds","score":0.8759999871253967},{"id":"https://openalex.org/keywords/stochastic-convex-optimization","display_name":"stochastic convex optimization","score":0.8149999976158142},{"id":"https://openalex.org/keywords/regularization-parameter","display_name":"regularization parameter","score":0.9769999980926514},{"id":"https://openalex.org/keywords/adam-optimizer","display_name":"Adam optimizer","score":0.5989999771118164},{"id":"https://openalex.org/keywords/adamw-optimizer","display_name":"AdamW optimizer","score":0.6669999957084656},{"id":"https://openalex.org/keywords/memory-errors","display_name":"memory errors","score":0.5649999976158142}],"concepts":[{"id":"https://openalex.org/C8642999","wikidata":"https://www.wikidata.org/wiki/Q4171168","display_name":"Hyperparameter","level":2,"score":0.6470999717712402},{"id":"https://openalex.org/C114466953","wikidata":"https://www.wikidata.org/wiki/Q6034165","display_name":"Initialization","level":2,"score":0.5895000100135803},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.5633000135421753},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5604000091552734},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5501000285148621},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5285000205039978},{"id":"https://openalex.org/C179254644","wikidata":"https://www.wikidata.org/wiki/Q13222844","display_name":"Moment (physics)","level":2,"score":0.5246999859809875},{"id":"https://openalex.org/C206688291","wikidata":"https://www.wikidata.org/wiki/Q7617819","display_name":"Stochastic gradient descent","level":3,"score":0.4977000057697296},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4490000009536743},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.44020000100135803},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.43290001153945923},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.4131999909877777},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.39750000834465027},{"id":"https://openalex.org/C55479107","wikidata":"https://www.wikidata.org/wiki/Q97663916","display_name":"Stochastic approximation","level":3,"score":0.3971000015735626},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.38940000534057617},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.3734000027179718},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.37139999866485596},{"id":"https://openalex.org/C115680565","wikidata":"https://www.wikidata.org/wiki/Q5977448","display_name":"Gradient method","level":2,"score":0.34220001101493835},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.34139999747276306},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.334199994802475},{"id":"https://openalex.org/C167928553","wikidata":"https://www.wikidata.org/wiki/Q1376021","display_name":"Estimation theory","level":2,"score":0.33309999108314514},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.3262999951839447},{"id":"https://openalex.org/C202286095","wikidata":"https://www.wikidata.org/wiki/Q579262","display_name":"Error function","level":2,"score":0.3224000036716461},{"id":"https://openalex.org/C39613435","wikidata":"https://www.wikidata.org/wiki/Q846677","display_name":"Remainder","level":2,"score":0.3174000084400177},{"id":"https://openalex.org/C103088060","wikidata":"https://www.wikidata.org/wiki/Q1062839","display_name":"Error detection and correction","level":2,"score":0.31610000133514404},{"id":"https://openalex.org/C194387892","wikidata":"https://www.wikidata.org/wiki/Q1747770","display_name":"Stochastic optimization","level":2,"score":0.30630001425743103},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.2985000014305115},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.29760000109672546},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2955000102519989},{"id":"https://openalex.org/C10494615","wikidata":"https://www.wikidata.org/wiki/Q17086765","display_name":"Proximal Gradient Methods","level":4,"score":0.2946000099182129},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.2897000014781952},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.2800999879837036},{"id":"https://openalex.org/C122383733","wikidata":"https://www.wikidata.org/wiki/Q865920","display_name":"Approximation error","level":2,"score":0.26969999074935913},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.26649999618530273},{"id":"https://openalex.org/C75235859","wikidata":"https://www.wikidata.org/wiki/Q582659","display_name":"Exponential growth","level":2,"score":0.2623000144958496},{"id":"https://openalex.org/C95763700","wikidata":"https://www.wikidata.org/wiki/Q578985","display_name":"Convergence of random variables","level":3,"score":0.26030001044273376},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.2597000002861023},{"id":"https://openalex.org/C55660270","wikidata":"https://www.wikidata.org/wiki/Q5164377","display_name":"Constrained optimization","level":2,"score":0.2547000050544739},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.2542000114917755}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.30382","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.30382","pdf_url":"https://arxiv.org/pdf/2608.30382","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.2608.30382","doi":"https://doi.org/10.48550/arxiv.2608.30382","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.30382","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":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2608.30382","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.30382","pdf_url":"https://arxiv.org/pdf/2608.30382","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/G1652504919","display_name":null,"funder_award_id":"EXC 2044","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G2817606592","display_name":"EXC 2044: Mathematik M\u00fcnster: Dynamik \u2013 Geometrie \u2013 Struktur","funder_award_id":"390685587","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7204886889.pdf","grobid_xml":"https://content.openalex.org/works/W7204886889.grobid-xml"},"referenced_works_count":27,"referenced_works":["https://openalex.org/W2523246573","https://openalex.org/W2662617432","https://openalex.org/W2785523195","https://openalex.org/W2894692220","https://openalex.org/W2908510526","https://openalex.org/W2963698657","https://openalex.org/W2964121744","https://openalex.org/W3086677109","https://openalex.org/W4323076471","https://openalex.org/W4388092179","https://openalex.org/W4388184679","https://openalex.org/W4400611422","https://openalex.org/W4400870676","https://openalex.org/W4401306300","https://openalex.org/W4414374557","https://openalex.org/W4415085230","https://openalex.org/W4416895734","https://openalex.org/W7105031866","https://openalex.org/W7118412265","https://openalex.org/W7133212049","https://openalex.org/W7133223833","https://openalex.org/W7133238359","https://openalex.org/W7139966452","https://openalex.org/W7161151772","https://openalex.org/W7166638517","https://openalex.org/W7167594533","https://openalex.org/W7167607350"],"related_works":["https://openalex.org/W7139966452","https://openalex.org/W7201914068","https://openalex.org/W4400870676","https://openalex.org/W7079467925","https://openalex.org/W4391505457","https://openalex.org/W2894692220","https://openalex.org/W3132287789","https://openalex.org/W4393924640","https://openalex.org/W4288445096","https://openalex.org/W4416895734"],"abstract_inverted_index":{"Popular":[0],"adaptive":[1,36],"stochastic":[2,144,196],"gradient":[3,257],"descent":[4],"(SGD)":[5],"methods":[6,37,121],"to":[7,59,63,83,87,115,135,155],"train":[8],"artificial":[9],"intelligence":[10],"(AI)":[11],"systems":[12],"include":[13],"the":[14,16,19,23,42,73,103,123,133,136,140,149,165,168,172,176,182,192,213,224,227,234,273,284],"RMSprop,":[15],"Adam,":[17],"and":[18,28,55,72,93,96,202,233],"AdamW":[20,29],"optimizers,":[21],"where":[22],"adaptivity":[24],"parts":[25],"in":[26,68,98,139,191,272,288],"Adam":[27],"basically":[30],"just":[31,247],"coincide":[32],"with":[33,122,132,212,260],"RMSprop.":[34,161,289],"Such":[35],"involve":[38],"several":[39],"hyperparameters":[40],"including":[41],"regularization":[43,235],"parameter":[44,77,231,236],"$\u03b5$":[45],"(which":[46,79],"ensures":[47],"that":[48,188],"one":[49],"does":[50],"not":[51,127,246],"divide":[52],"by":[53,70,100,181],"0":[54],"is":[56,80,148],"often":[57,81],"chosen":[58,82],"be":[60,84],"very":[61,85],"close":[62,86],"zero":[64],"such":[65,89,107,120],"as":[66,90],"$10^{-8}$":[67],"PyTorch":[69,99],"default)":[71],"second":[74,228,285],"moment":[75,229,281,286],"decay":[76,230],"$\u03b2$":[78,232],"$1$":[88],"0.99":[91],"(RMSprop)":[92],"0.999":[94],"(Adam":[95],"AdamW)":[97],"default).":[101],"Despite":[102],"high":[104],"relevance":[105],"of":[106,142,152,167,171,184,199,206,223,275],"methods,":[108],"it":[109],"remains":[110],"an":[111,185],"open":[112],"research":[113],"problem":[114,159],"provide":[116],"error":[117,124,205,214,243,262],"estimates":[118,244],"for":[119,160,248,255,283],"constants":[125,215,263],"being":[126,216,264],"exploding":[128],"but":[129,253],"uniformly":[130,217],"bounded":[131],"respect":[134],"hyperparameters,":[137],"even":[138],"situation":[141],"convex":[143],"optimization":[145],"problems.":[146],"It":[147],"key":[150,268],"contribution":[151],"this":[153,158],"work":[154],"essentially":[156],"solve":[157],"Specifically,":[162],"we":[163],"bound":[164],"expectation":[166],"stopped":[169],"evaluation":[170],"objective":[173],"function":[174],"at":[175],"RMSprop":[177],"process":[178,287],"from":[179],"above":[180],"sum":[183],"initialization":[186],"term":[187],"decays":[189],"exponentially":[190],"training":[193],"time,":[194],"a":[195,203],"approximation":[197],"remainder":[198],"order":[200,207],"$\u03b3_n$,":[201],"memory":[204],"$(":[208],"1":[209],"-":[210],"\u03b2)^2$":[211],"controlled":[218],"over":[219],"all":[220,249,261],"admissible":[221],"choices":[222],"step":[225,258],"sizes,":[226],"$\u03b5\\in[0,1]$":[237],"(also":[238],"covering":[239],"$\u03b5=0$).":[240],"Our":[241],"non-asymptotic":[242],"hold":[245,254],"sufficiently":[250],"large":[251],"n":[252],"every":[256],"$n=1,2,3,...$":[259],"explicitly":[265],"specified.":[266],"The":[267],"innovative":[269],"new":[270],"feature":[271],"proof":[274],"our":[276],"analysis":[277],"are":[278],"suitable":[279],"inverse":[280],"bounds":[282]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-02T00:00:00"}
