  This paper is devoted to the study (common in many applications) of the
black-box optimization problem, where the black-box represents a gradient-free
oracle $\tilde{f} = f(x) + \xi$ providing the objective function value with
some stochastic noise. Assuming that the objective function is $\mu$-strongly
convex, and also not just $L$-smooth, but has a higher order of smoothness
($\beta \geq 2$) we provide a novel optimization method: Zero-Order Accelerated
Batched Stochastic Gradient Descent, whose theoretical analysis closes the
question regarding the iteration complexity, achieving optimal estimates.
Moreover, we provide a thorough analysis of the maximum noise level, and show
under which condition the maximum noise level will take into account
information about batch size $B$ as well as information about the smoothness
order of the function $\beta$.
