<p>Covariate shift refers to the change in the distribution of input data (covariates) between the training and testing phases of a machine learning model. Standard regression typically assumes that training and testing samples come from the same distribution, an assumption that often fails in practice. Various methods have been developed to address covariate shift, with importance weighting being one of the most widely used. While existing literature under covariate shift primarily focuses on batch learning, the high algorithmic complexity of these methods can significantly hinder their performance in big data scenarios. In contrast, online learning processes data incrementally, updating outputs in real time, which allows for more efficient handling of large-scale and streaming datasets. This paper explores the application of importance weighting correction for online learning algorithms in reproducing kernel Hilbert spaces under covariate shift. Our findings demonstrate fast convergence rates for the reweighted online learning algorithms, particularly when the importance weight function has a finite second moment.</p>