{"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/global-optimization-of-lipschitz-functions","title":"Global optimization of Lipschitz functions","arxiv_id":"1703.02628","date":"2017-03-07","proceeding":"ICML 2017 8","authors":["Cédric Malherbe","Nicolas Vayatis"],"abstract":"The goal of the paper is to design sequential strategies which lead to\nefficient optimization of an unknown function under the only assumption that it\nhas a finite Lipschitz constant. We first identify sufficient conditions for\nthe consistency of generic sequential algorithms and formulate the expected\nminimax rate for their performance. We introduce and analyze a first algorithm\ncalled LIPO which assumes the Lipschitz constant to be known. Consistency,\nminimax rates for LIPO are proved, as well as fast rates under an additional\nH\\\"older like condition. An adaptive version of LIPO is also introduced for the\nmore realistic setup where the Lipschitz constant is unknown and has to be\nestimated along with the optimization. Similar theoretical guarantees are shown\nto hold for the adaptive LIPO algorithm and a numerical assessment is provided\nat the end of the paper to illustrate the potential of this strategy with\nrespect to state-of-the-art methods over typical benchmark problems for global\noptimization.","url_abs":"http://arxiv.org/abs/1703.02628v3","url_pdf":"http://arxiv.org/pdf/1703.02628v3.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":"global-optimization-of-lipschitz-functions","repo_url":"https://github.com/Sycor4x/lipo","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"global-optimization-of-lipschitz-functions","repo_url":"https://github.com/gaetanserre/lean-lipo","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}},{"paper_slug":"global-optimization-of-lipschitz-functions","repo_url":"https://github.com/leonidk/physical_simulation","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"Zlib"}}],"tasks":[{"task_slug":"hyperparameter-optimization","task_name":"Hyperparameter Optimization"},{"task_slug":"global-optimization","task_name":"global-optimization"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/1703.02628","atlas_url":"https://app.syntology.ai/?focus=1703.02628","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"1703.02628"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-25T09:33:49+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. 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