  A typical approach in estimating the learning rate of a regularized learning
scheme is to bound the approximation error by the sum of the sampling error,
the hypothesis error and the regularization error. Using a reproducing kernel
space that satisfies the linear representer theorem brings the advantage of
discarding the hypothesis error from the sum automatically. Following this
direction, we illustrate how reproducing kernel Banach spaces with the l1 norm
can be applied to improve the learning rate estimate of l1-regularization in
machine learning.
