The application of a zeroth-order scheme for minimising Polyak-\L{}ojasewicz (PL) functions is considered. The framework is based on exploiting a random oracle to estimate the function gradient. The convergence of the algorithm to a global minimum in the unconstrained case and to a neighbourhood of the global minimum in the constrained case along with their corresponding complexity bounds are presented. The theoretical results are demonstrated via numerical examples.
Cite
@article{arxiv.2405.09106,
title = {Minimisation of Polyak-\L{}ojasewicz Functions Using Random Zeroth-Order Oracles},
author = {Amir Ali Farzin and Iman Shames},
journal= {arXiv preprint arXiv:2405.09106},
year = {2025}
}