Zeroth-order methods for noisy Hölder-gradient functions

In this paper, we prove new complexity bounds for zeroth-order methods in non-convex optimization with inexact observations of the objective function values. We use Gaussian smoothing approach Nesterov and Spokoiny(Found Comput Math 17(2): 527–566, 2015. https://doi.org/10.1007/s10208-015-9296-2 ) extend their results, obtained smooth problems, to setting minimization functions Hölder-continuous gradient noisy oracle, obtaining noise upper-bounds as well. consider finite-difference approximation based on normally distributed random vectors that descent scheme converges stationary point smoothed function. also convergence original (not smoothed) obtain number steps algorithm making norm its small. Additionally provide level oracle which it is still possible guarantee above hold. separately case $$\nu = 1$$ show dependence dimension can be improved.