In this paper, we study the black box optimization problem under the Polyak--Lojasiewicz (PL) condition, assuming that the objective function is not just smooth, but has higher smoothness. By using "kernel-based" approximation instead of the exact gradient in Stochastic Gradient Descent method, we improve the best known results of convergence in the class of gradient-free algorithms solving problem under PL condition. We generalize our results to the case where a zero-order oracle returns a function value at a point with some adversarial noise. We verify our theoretical results on the example of solving a system of nonlinear equations.
@article{arxiv.2305.15828,
title = {Highly Smoothness Zero-Order Methods for Solving Optimization Problems under PL Condition},
author = {Aleksandr Lobanov and Alexander Gasnikov and Fedor Stonyakin},
journal= {arXiv preprint arXiv:2305.15828},
year = {2023}
}