  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.
