In this paper we work on the estimation of a regression function that belongs to a polynomial decay reproducing kernel Hilbert space (RKHS). We describe spectral filter framework for our estimator that allows us to deal with several iterative algorithms: gradient descent, Tikhonov regularization, etc. The main goal of the paper is to propose a new early stopping rule by introducing smoothing parameter for empirical risk of the estimator in order to improve the previous results [1] on discrepancy principle. Theoretical justifications as well as simulations experiments for the proposed rule are provided.