  We deal with pointwise approximation of solutions of scalar stochastic
differential equations in the presence of informational noise about underlying
drift and diffusion coefficients. We define a randomized derivative-free
version of Milstein algorithm $\mathcal{\bar A}^{df-RM}_n$ and investigate its
error. We also study lower bounds on the error of an arbitrary algorithm. It
turns out that in some case the scheme $\mathcal{\bar A}^{df-RM}_n$ is the
optimal one. Finally, in order to test the algorithm $\mathcal{\bar
A}^{df-RM}_n$ in practice, we report performed numerical experiments.
