  In recent years, transfer learning has garnered significant attention in the
machine learning community. Its ability to leverage knowledge from related
studies to improve generalization performance in a target study has made it
highly appealing. This paper focuses on investigating the transfer learning
problem within the context of nonparametric regression over a reproducing
kernel Hilbert space. The aim is to bridge the gap between practical
effectiveness and theoretical guarantees. We specifically consider two
scenarios: one where the transferable sources are known and another where they
are unknown. For the known transferable source case, we propose a two-step
kernel-based estimator by solely using kernel ridge regression. For the unknown
case, we develop a novel method based on an efficient aggregation algorithm,
which can automatically detect and alleviate the effects of negative sources.
This paper provides the statistical properties of the desired estimators and
establishes the minimax optimal rate. Through extensive numerical experiments
on synthetic data and real examples, we validate our theoretical findings and
demonstrate the effectiveness of our proposed method.
