  In this work we investigate the variation of the online kernelized ridge
regression algorithm in the setting of $d-$dimensional adversarial
nonparametric regression. We derive the regret upper bounds on the classes of
Sobolev spaces $W_{p}^{\beta}(\mathcal{X})$, $p\geq 2, \beta>\frac{d}{p}$. The
upper bounds are supported by the minimax regret analysis, which reveals that
in the cases $\beta> \frac{d}{2}$ or $p=\infty$ these rates are (essentially)
optimal. Finally, we compare the performance of the kernelized ridge regression
forecaster to the known non-parametric forecasters in terms of the regret rates
and their computational complexity as well as to the excess risk rates in the
setting of statistical (i.i.d.) nonparametric regression.
