Accelerating Single-Point Zeroth-Order Optimization with Regression-Based Gradient Surrogates

[2507.04223] Accelerating Single-Point Zeroth-Order Optimization with Regression-Based Gradient Surrogates Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Optimization and Control arXiv:2507.04223 (math) [Submitted on 6 Jul 2025 ( v1 ), last revised 14 Aug 2026 (this version, v3)] Title: Accelerating Single-Point Zeroth-Order Optimization with Regression-Based Gradient Surrogates Authors: Xin Chen , Zhaolin Ren View a PDF of the paper titled Accelerating Single-Point Zeroth-Order Optimization with Regression-Based Gradient Surrogates, by Xin Chen and Zhaolin Ren View PDF HTML (experimental) Abstract: Zeroth-order optimization (ZO) is widely used for solving black-box optimization and control problems. In particular, single-point ZO (SZO) is well-suited to online or dynamic problem settings due to its requirement of only a single function evaluation per iteration. However, SZO suffers from high gradient estimation variance and slow convergence, which severely limit its practical applicability. To overcome this limitation, we propose a novel yet simple SZO framework termed regression-based SZO (ReSZO), which substantially enhances the convergence rate. Specifically, ReSZO constructs a surrogate function via regression using historical function evaluations and employs the gradient of this surrogate function for iterative updates. Two instantiations of ReSZO, which fit linear and quadratic surrogate functions respectively, are introduced. Moreover, we provide a non-asymptotic convergence analysis for the linear instantiation of ReSZO, showing that its convergence rates are comparable to those of two-point ZO methods. Extensive numerical experiments demonstrate that ReSZO empirically converges two to three times faster than two-point ZO in terms of function query complexity. Subjects: Optimization and Control (math.OC) Cite as: arXiv:2507.04223 [math.OC] (or arXiv:2507.04223v3 [math.OC] for this version) https://doi.org/10.48550/arXiv.2507.04223 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Xin Chen [ view email ] [v1] Sun, 6 Jul 2025 03:26:52 UTC (747 KB) [v2] Thu, 5 Feb 2026 04:03:45 UTC (432 KB) [v3] Fri, 14 Aug 2026 21:46:38 UTC (475 KB) Full-text links: Access Paper: View a PDF of the paper titled Accelerating Single-Point Zeroth-Order Optimization with Regression-Based Gradient Surrogates, by Xin Chen and Zhaolin Ren View PDF HTML (experimental) TeX Source view license Current browse context: math.OC < prev | next > new | recent | 2025-07 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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