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 10⁹ kicks and determine the exponent α 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 α drops with increasing d. We also argue that the renormalization arguments proposed by Cherroret N et al (arXiv:1401.1038) are not valid for this model and the Anderson model with local nonlinearity in d = 3.