Fully Zeroth-Order Bilevel Programming via Gaussian Smoothing

arXiv:2404.00158v1 Announce Type: cross
Abstract: 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 …

abstract algorithms analyze approximation arxiv cs.lg derivatives functions gradient identity math.oc paper programming stochastic study type unbiased values via