  This paper is devoted to solving a convex stochastic optimization problem in
a overparameterization setup for the case where the original gradient
computation is not available, but an objective function value can be computed.
For this class of problems we provide a novel gradient-free algorithm, whose
creation approach is based on applying a gradient approximation with $l_2$
randomization instead of a gradient oracle in the biased Accelerated SGD
algorithm, which generalizes the convergence results of the AC-SA algorithm to
the case where the gradient oracle returns a noisy (inexact) objective function
value. We also perform a detailed analysis to find the maximum admissible level
of adversarial noise at which we can guarantee to achieve the desired accuracy.
We verify the theoretical results of convergence using a model example.
