mlsanityData to 7 Oct 2026

Global optimization of Lipschitz functions

arXiv 1703.02628 ↗First posted 7 Mar 2017stat.MLcited by 39

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Abstract (arXiv)

The goal of the paper is to design sequential strategies which lead to efficient optimization of an unknown function under the only assumption that it has a finite Lipschitz constant. We first identify sufficient conditions for the consistency of generic sequential algorithms and formulate the expected minimax rate for their performance. We introduce and analyze a first algorithm called LIPO which assumes the Lipschitz constant to be known. Consistency, minimax rates for LIPO are proved, as well as fast rates under an additional H"older like condition. An adaptive version of LIPO is also introduced for the more realistic setup where the Lipschitz constant is unknown and has to be estimated along with the optimization. Similar theoretical guarantees are shown to hold for the adaptive LIPO algorithm and a numerical assessment is provided at the end of the paper to illustrate the potential of this strategy with respect to state-of-the-art methods over typical benchmark problems for global optimization.

Key facts. Cited by 39 papers in the map (data through 7 Oct 2026). First posted on arXiv 7 Mar 2017.

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Citing papers per year: 2021: 11; 2022: 8; 2023: 7; 2024: 6; 2025: 4; 2026: 3.

39 papers.

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  11. 2021Instance-Dependent Bounds for Zeroth-order Lipschitz Optimization with Error Certificatescited by 7
  12. 2022Global Optimization with Parametric Function Approximationcited by 7
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  11. 2021Wave-Informed Matrix Factorization with Global Optimality Guaranteescited by 1
  12. 2022Combining Lipschitz and RBF Surrogate Models for High-dimensional Computationally Expensive Problemscited by 1
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