  This paper is devoted to the study of the solution of a stochastic convex
black box optimization problem. Where the black box problem means that the
gradient-free oracle only returns the value of objective function, not its
gradient. We consider non-smooth and smooth setting of the solution to the
black box problem under adversarial stochastic noise. For two techniques
creating gradient-free methods: smoothing schemes via $L_1$ and $L_2$
randomizations, we find the maximum allowable level of adversarial stochastic
noise that guarantees convergence. Finally, we analyze the convergence behavior
of the algorithms under the condition of a large value of noise level.
