Regularization in kernel learning

TL;DR

This paper establishes optimal error rates for kernel learning with regularization in RKHS, demonstrating that slower-growing regularization terms can achieve strong generalization guarantees.

Contribution

It introduces a novel analysis showing that regularization terms growing slower than quadratic still attain optimal error bounds in kernel learning.

Findings

Achieves best known error rates under mild kernel assumptions.

Proves regularization can grow slower than quadratic in RKHS norm.

Enhances understanding of regularization effects in kernel methods.

Abstract

Under mild assumptions on the kernel, we obtain the best known error rates in a regularized learning scenario taking place in the corresponding reproducing kernel Hilbert space (RKHS). The main novelty in the analysis is a proof that one can use a regularization term that grows significantly slower than the standard quadratic growth in the RKHS norm.