{"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/curvature-aware-derivative-free-optimization","title":"Curvature-Aware Derivative-Free Optimization","arxiv_id":"2109.13391","date":"2021-09-27","proceeding":null,"authors":["Bumsu Kim","HanQin Cai","Daniel Mckenzie","Wotao Yin"],"abstract":"The paper discusses derivative-free optimization (DFO), which involves minimizing a function without access to gradients or directional derivatives, only function evaluations. Classical DFO methods, which mimic gradient-based methods, such as Nelder-Mead and direct search have limited scalability for high-dimensional problems. Zeroth-order methods have been gaining popularity due to the demands of large-scale machine learning applications, and the paper focuses on the selection of the step size $\\alpha_k$ in these methods. The proposed approach, called Curvature-Aware Random Search (CARS), uses first- and second-order finite difference approximations to compute a candidate $\\alpha_{+}$. We prove that for strongly convex objective functions, CARS converges linearly provided that the search direction is drawn from a distribution satisfying very mild conditions. We also present a Cubic Regularized variant of CARS, named CARS-CR, which converges in a rate of $\\mathcal{O}(k^{-1})$ without the assumption of strong convexity. Numerical experiments show that CARS and CARS-CR match or exceed the state-of-the-arts on benchmark problem sets.","url_abs":"https://arxiv.org/abs/2109.13391v2","url_pdf":"https://arxiv.org/pdf/2109.13391v2.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":"abstracts"},"code_links":[{"paper_slug":"curvature-aware-derivative-free-optimization","repo_url":"https://github.com/bumsu-kim/CARS_Refactored","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":{"status":"ok"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":"https://app.syntology.ai/?focus=2109.13391","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}