In this paper

we investigate the regularized least-square regression problem by making use of empirical covering numbers and the projection operator.Learning rates are conducted based on these techniques.Comparing with existing results

we simplify the theoretical analysis.Moreover

learning rates are also improved under mild conditions.Concretely speaking

the learning rates we obtained are of type O（m-1）

which are regarded as the optimal learning rates on the generalization errors in learning theory literature.Meanwhile

we abandon the widely adopted iteration methods when deriving the generalization errors.