Online nonparametric regression with Sobolev kernels

Abstract

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^(X), p 2, >dp. The upper bounds are supported by the minimax regret analysis, which reveals that in the cases > d2 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.

Tasks

Reproductions