Optimal Two-Step Stepsize Schedule for Stochastic Gradient Methods

[2608.15035] Optimal Two-Step Stepsize Schedule for Stochastic Gradient Methods Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Optimization and Control arXiv:2608.15035 (math) [Submitted on 15 Aug 2026] Title: Optimal Two-Step Stepsize Schedule for Stochastic Gradient Methods Authors: Luwei Bai , Baoyu Zhou View a PDF of the paper titled Optimal Two-Step Stepsize Schedule for Stochastic Gradient Methods, by Luwei Bai and Baoyu Zhou View PDF HTML (experimental) Abstract: Structured nonconstant large stepsizes can improve the convergence of gradient descent in the deterministic setting. However, in stochastic optimization, aggressive stepsizes can amplify oracle noise and hinder the convergence of stochastic gradient methods. We characterize the globally optimal two-step stepsize schedule for stochastic gradient methods applied to strongly convex and smooth functions, assuming access only to unbiased stochastic gradient estimates with finite support and bounded variance. The optimal schedule depends on the ratio of the initial optimality gap to the noise level and exhibits several distinct regimes. As the influence of stochastic noise diminishes, the optimal two-step stepsizes become larger, reflecting a balance between the benefits of faster iterate convergence and the perturbations induced by stochastic noise. Comments: 23 pages, 2 figures Subjects: Optimization and Control (math.OC) MSC classes: 90C25, 90C30 Cite as: arXiv:2608.15035 [math.OC] (or arXiv:2608.15035v1 [math.OC] for this version) https://doi.org/10.48550/arXiv.2608.15035 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Baoyu Zhou [ view email ] [v1] Sat, 15 Aug 2026 04:39:29 UTC (247 KB) Full-text links: Access Paper: View a PDF of the paper titled Optimal Two-Step Stepsize Schedule for Stochastic Gradient Methods, by Luwei Bai and Baoyu Zhou View PDF HTML (experimental) TeX Source view license Current browse context: math.OC < prev | next > new | recent | 2026-08 Change to browse by: math References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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