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Convergence Rates of Zeroth Order Gradient Descent for Łojasiewicz Functions

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  • Tianyu Wang

    (Shanghai Center for Mathematical Sciences, Fudan University, Shanghai 200437, China; Shanghai Artificial Intelligence Laboratory, Shanghai 200232, China)

  • Yasong Feng

    (Shanghai Center for Mathematical Sciences, Fudan University, Shanghai 200437, China)

Abstract

We prove convergence rates of Zeroth-order Gradient Descent (ZGD) algorithms for Łojasiewicz functions. Our results show that for smooth Łojasiewicz functions with Łojasiewicz exponent larger than 0.5 and smaller than 1, the functions values can converge much faster than the (zeroth-order) gradient descent trajectory. Similar results hold for convex nonsmooth Łojasiewicz functions.

Suggested Citation

  • Tianyu Wang & Yasong Feng, 2024. "Convergence Rates of Zeroth Order Gradient Descent for Łojasiewicz Functions," INFORMS Journal on Computing, INFORMS, vol. 36(6), pages 1611-1633, December.
    • Handle: RePEc:inm:orijoc:v:36:y:2024:i:6:p:1611-1633
    DOI: 10.1287/ijoc.2023.0247
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    References listed on IDEAS

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    1. NESTEROV, Yurii & POLYAK, B.T., 2006. "Cubic regularization of Newton method and its global performance," LIDAM Reprints CORE 1927, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Yurii NESTEROV & Vladimir SPOKOINY, 2017. "Random gradient-free minimization of convex functions," LIDAM Reprints CORE 2851, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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