Fully Zeroth-Order Bilevel Programming via Gaussian Smoothing
<|reference_start|>Fully Zeroth-Order Bilevel Programming via Gaussian Smoothing: In this paper, we study and analyze zeroth-order stochastic approximation algorithms for solving bilvel 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 used 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.<|reference_end|>
@article{aghasi2024fully,
    title={Fully Zeroth-Order Bilevel Programming via Gaussian Smoothing},
    author={Alireza Aghasi, Saeed Ghadimi},
    journal={arXiv preprint arXiv:2404.00158},
    year={2024},
    archivePrefix={arXiv},
    eprint={2404.00158},
    primaryClass={math.OC cs.LG}
}