Online nonparametric regression with Sobolev kernels

02/06/2021

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by   Oleksandr Zadorozhnyi, et al.

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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^β(𝒳), p≥ 2, β>d/p. The upper bounds are supported by the minimax regret analysis, which reveals that in the cases β> d/2 or p=∞ 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.