{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/fully-adaptive-zeroth-order-method-for","title":"Fully Adaptive Zeroth-Order Method for Minimizing Functions with Compressible Gradients","arxiv_id":"2501.11616","date":"2025-01-20","proceeding":null,"authors":["Geovani Nunes Grapiglia","Daniel McKenzie"],"abstract":"We propose an adaptive zeroth-order method for minimizing differentiable functions with $L$-Lipschitz continuous gradients. The method is designed to take advantage of the eventual compressibility of the gradient of the objective function, but it does not require knowledge of the approximate sparsity level $s$ or the Lipschitz constant $L$ of the gradient. We show that the new method performs no more than $O\\left(n^{2}\\epsilon^{-2}\\right)$ function evaluations to find an $\\epsilon$-approximate stationary point of an objective function with $n$ variables. Assuming additionally that the gradients of the objective function are compressible, we obtain an improved complexity bound of $O\\left(s\\log\\left(n\\right)\\epsilon^{-2}\\right)$ function evaluations, which holds with high probability. Preliminary numerical results illustrate the efficiency of the proposed method and demonstrate that it can significantly outperform its non-adaptive counterpart.","url_abs":"https://arxiv.org/abs/2501.11616v2","url_pdf":"https://arxiv.org/pdf/2501.11616v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"fully-adaptive-zeroth-order-method-for","repo_url":"https://github.com/mines-opt-ml/zoro-fa","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}