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Convergence Rates of Zeroth Order Gradient Descent for Łojasiewicz Functions

Author

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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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