  We study numerically the frequency modulated kicked nonlinear rotator with
effective dimension $d=1,2,3,4$. We follow the time evolution of the model up
to $10^9$ kicks and determine the exponent $\alpha$ of subdiffusive spreading
which changes from $0.35$ to $0.5$ when the dimension changes from $d=1$ to
$4$. All results are obtained in a regime of relatively strong Anderson
localization well below the Anderson transition point existing for $d=3,4$. We
explain that this variation of the exponent is different from the usual
$d-$dimensional Anderson models with local nonlinearity where $\alpha$ drops
with increasing $d$. We also argue that the renormalization arguments proposed
by Cherroret N et al. arXiv:1401.1038 are not valid.
