  In this paper, we investigate the problem of strong approximation of the
solution of SDEs in the case when the drift coefficient is given in the
integral form. Such drift often appears when analyzing stochastic dynamics of
optimization procedures in machine learning problems. We discuss connections of
the defined randomized Euler approximation scheme with the perturbed version of
the stochastic gradient descent (SGD) algorithm. We investigate its upper error
bounds, in terms of the discretization parameter n and the size M of the random
sample drawn at each step of the algorithm, in different subclasses of
coefficients of the underlying SDE. Finally, the results of numerical
experiments performed by using GPU architecture are also reported.
