Аннотация:
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” approximations instead of the exact gradient in the Stochastic Gradient Descent method, we improve the best-known results of convergence in the class of gradient-free algorithms solving problems under the PL condition. We generalize our results to the case where a zeroth-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.
Ключевые слова:black-box optimization, gradient-free methods, kernel approximation, maximum noise level.
Поступила в редакцию: 05.11.2023 Принята в печать: 07.06.2024