The improved learning rate for regularized regression with RKBSs

The investigation on the performance of learning from samples of functions in Banach spaces is a new research field. A key theoretical problem we need to investigate is how the convergence rate is influenced by the geometry property of the Banach spaces. In the present paper, we provide the learning rate for the kernel regularized regression based on reproducing kernel Banach spaces. The rate is provided in both expected mean and empirical mean. The results show that the uniform convexity influences the learning rate.