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Fully Zeroth-Order Bilevel Programming via Gaussian Smoothing

Author

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  • Alireza Aghasi

    (Oregon State University)

  • Saeed Ghadimi

    (University of Waterloo)

Abstract

In this paper, we study and analyze zeroth-order stochastic approximation algorithms for solving bilevel problems when neither the upper/lower objective values nor their unbiased gradient estimates are available. In particular, exploiting Stein’s identity, we first use Gaussian smoothing to estimate first- and second-order partial derivatives of functions with two independent block of variables. We then use these estimates in the framework of a stochastic approximation algorithm for solving bilevel optimization problems and establish its non-asymptotic convergence analysis. To the best of our knowledge, this is the first time that sample complexity bounds are established for a fully stochastic zeroth-order bilevel optimization algorithm.

Suggested Citation

  • Alireza Aghasi & Saeed Ghadimi, 2025. "Fully Zeroth-Order Bilevel Programming via Gaussian Smoothing," Journal of Optimization Theory and Applications, Springer, vol. 205(2), pages 1-39, May.
    • Handle: RePEc:spr:joptap:v:205:y:2025:i:2:d:10.1007_s10957-025-02647-y
    DOI: 10.1007/s10957-025-02647-y
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    References listed on IDEAS

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    4. 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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