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 $W_{p}^{beta}(mathcal{X})$, $pgeq 2, beta>frac{d}{p}$. 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.
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