{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,14]],"date-time":"2026-04-14T08:48:29Z","timestamp":1776156509144,"version":"3.50.1"},"reference-count":20,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T00:00:00Z","timestamp":1777593600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T00:00:00Z","timestamp":1777593600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T00:00:00Z","timestamp":1777593600000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-017"},{"start":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T00:00:00Z","timestamp":1777593600000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"},{"start":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T00:00:00Z","timestamp":1777593600000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-012"},{"start":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T00:00:00Z","timestamp":1777593600000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T00:00:00Z","timestamp":1777593600000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-004"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12501704"],"award-info":[{"award-number":["12501704"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003399","name":"Science and Technology Commission of Shanghai Municipality","doi-asserted-by":"publisher","award":["24YF2702500"],"award-info":[{"award-number":["24YF2702500"]}],"id":[{"id":"10.13039\/501100003399","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Systems &amp; Control Letters"],"published-print":{"date-parts":[[2026,5]]},"DOI":"10.1016\/j.sysconle.2026.106419","type":"journal-article","created":{"date-parts":[[2026,3,16]],"date-time":"2026-03-16T06:17:46Z","timestamp":1773641866000},"page":"106419","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"C","title":["Revisiting stochastic gradient descent for strongly convex objectives: Tight uniform-in-time bounds"],"prefix":"10.1016","volume":"212","author":[{"ORCID":"https:\/\/orcid.org\/0009-0007-1041-7626","authenticated-orcid":false,"given":"Kang","family":"Chen","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0003-8274-3560","authenticated-orcid":false,"given":"Yasong","family":"Feng","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6206-8359","authenticated-orcid":false,"given":"Tianyu","family":"Wang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"78","reference":[{"key":"10.1016\/j.sysconle.2026.106419_b1","series-title":"Breaking a logarithmic barrier in the stopping time convergence rate of stochastic first-order methods","author":"Feng","year":"2025"},{"issue":"3","key":"10.1016\/j.sysconle.2026.106419_b2","doi-asserted-by":"crossref","first-page":"400","DOI":"10.1214\/aoms\/1177729586","article-title":"A stochastic approximation method","volume":"22","author":"Robbins","year":"1951","journal-title":"Ann. Math. Stat."},{"issue":"3","key":"10.1016\/j.sysconle.2026.106419_b3","doi-asserted-by":"crossref","first-page":"462","DOI":"10.1214\/aoms\/1177729392","article-title":"Stochastic estimation of the maximum of a regression function","volume":"23","author":"Kiefer","year":"1952","journal-title":"Ann. Math. Stat."},{"key":"10.1016\/j.sysconle.2026.106419_b4","volume":"vol. 1","author":"Lan","year":"2020"},{"key":"10.1016\/j.sysconle.2026.106419_b5","unstructured":"Z. Liu, Z. Zhou, Revisiting the Last-Iterate Convergence of Stochastic Gradient Methods, in: The Twelfth International Conference on Learning Representations, 2024."},{"issue":"4","key":"10.1016\/j.sysconle.2026.106419_b6","doi-asserted-by":"crossref","first-page":"411","DOI":"10.1287\/stsy.2022.0097","article-title":"Concentration of contractive stochastic approximation and reinforcement learning","volume":"12","author":"Chandak","year":"2022","journal-title":"Stoch. Syst."},{"issue":"2","key":"10.1016\/j.sysconle.2026.106419_b7","doi-asserted-by":"crossref","first-page":"1298","DOI":"10.1214\/24-AAP2143","article-title":"Concentration of contractive stochastic approximation: Additive and multiplicative noise","volume":"35","author":"Chen","year":"2025","journal-title":"Ann. Appl. Probab."},{"issue":"1","key":"10.1016\/j.sysconle.2026.106419_b8","doi-asserted-by":"crossref","first-page":"66","DOI":"10.1073\/pnas.58.1.66","article-title":"Confidence sequences for mean, variance, and median","volume":"58","author":"Darling","year":"1967","journal-title":"Proc. Natl. Acad. Sci."},{"key":"10.1016\/j.sysconle.2026.106419_b9","first-page":"265","article-title":"On confidence sequences","author":"Lai","year":"1976","journal-title":"Ann. Statist."},{"issue":"3","key":"10.1016\/j.sysconle.2026.106419_b10","doi-asserted-by":"crossref","first-page":"305","DOI":"10.1111\/j.2517-6161.1989.tb01433.x","article-title":"Interim analyses: the repeated confidence interval approach","volume":"51","author":"Jennison","year":"1989","journal-title":"J. R. Stat. Soc. Ser. B Stat. Methodol."},{"issue":"19","key":"10.1016\/j.sysconle.2026.106419_b11","doi-asserted-by":"crossref","first-page":"2355","DOI":"10.1080\/03610928408828831","article-title":"Incorporating scientific, ethical and economic considerations into the design of clinical trials in the pharmaceutical industry: A sequential approach","volume":"13","author":"Lai","year":"1984","journal-title":"Comm. Statist. Theory Methods"},{"key":"10.1016\/j.sysconle.2026.106419_b12","series-title":"Conference on Learning Theory","first-page":"423","article-title":"Lil\u2019ucb: An optimal exploration algorithm for multi-armed bandits","author":"Jamieson","year":"2014"},{"issue":"1","key":"10.1016\/j.sysconle.2026.106419_b13","first-page":"1","article-title":"On the complexity of best-arm identification in multi-armed bandit models","volume":"17","author":"Kaufmann","year":"2016","journal-title":"J. Mach. Learn. Res."},{"issue":"2","key":"10.1016\/j.sysconle.2026.106419_b14","doi-asserted-by":"crossref","first-page":"1055","DOI":"10.1214\/20-AOS1991","article-title":"Time-uniform, nonparametric, nonasymptotic confidence sequences","volume":"49","author":"Howard","year":"2021","journal-title":"Ann. Statist."},{"issue":"3","key":"10.1016\/j.sysconle.2026.106419_b15","doi-asserted-by":"crossref","first-page":"1806","DOI":"10.1287\/opre.2021.2135","article-title":"Always valid inference: Continuous monitoring of a\/b tests","volume":"70","author":"Johari","year":"2022","journal-title":"Oper. Res."},{"issue":"1","key":"10.1016\/j.sysconle.2026.106419_b16","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1093\/jrsssb\/qkad009","article-title":"Estimating means of bounded random variables by betting","volume":"86","author":"Waudby-Smith","year":"2024","journal-title":"J. R. Stat. Soc. Ser. B Stat. Methodol."},{"key":"10.1016\/j.sysconle.2026.106419_b17","series-title":"The Thirty Seventh Annual Conference on Learning Theory","first-page":"1486","article-title":"An information-theoretic lower bound in time-uniform estimation","author":"Duchi","year":"2024"},{"key":"10.1016\/j.sysconle.2026.106419_b18","series-title":"Neural Networks: Tricks of the Trade","first-page":"55","article-title":"Early stopping-but when?","author":"Prechelt","year":"2002"},{"key":"10.1016\/j.sysconle.2026.106419_b19","series-title":"Fine-tuning pretrained language models: Weight initializations, data orders, and early stopping","author":"Dodge","year":"2020"},{"key":"10.1016\/j.sysconle.2026.106419_b20","volume":"vol. 48","author":"Wainwright","year":"2019"}],"container-title":["Systems &amp; Control Letters"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0167691126000794?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0167691126000794?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,4,14]],"date-time":"2026-04-14T07:52:58Z","timestamp":1776153178000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0167691126000794"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,5]]},"references-count":20,"alternative-id":["S0167691126000794"],"URL":"https:\/\/doi.org\/10.1016\/j.sysconle.2026.106419","relation":{},"ISSN":["0167-6911"],"issn-type":[{"value":"0167-6911","type":"print"}],"subject":[],"published":{"date-parts":[[2026,5]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Revisiting stochastic gradient descent for strongly convex objectives: Tight uniform-in-time bounds","name":"articletitle","label":"Article Title"},{"value":"Systems & Control Letters","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.sysconle.2026.106419","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright","label":"Copyright"}],"article-number":"106419"}}