Fully Zeroth-Order Bilevel Programming via Gaussian Smoothing

Alireza Aghasi () and Saeed Ghadimi ()
Additional contact information
Alireza Aghasi: Oregon State University
Saeed Ghadimi: University of Waterloo

Journal of Optimization Theory and Applications, 2025, vol. 205, issue 2, No 12, 39 pages

Abstract: 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.

Keywords: Bilevel programming; Zeroth-order programming; Gaussian smoothing (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10957-025-02647-y Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:joptap:v:205:y:2025:i:2:d:10.1007_s10957-025-02647-y

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10957/PS2

DOI: 10.1007/s10957-025-02647-y

Access Statistics for this article

Journal of Optimization Theory and Applications is currently edited by Franco Giannessi and David G. Hull

More articles in Journal of Optimization Theory and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().