Abstract: We view regularized learning of a function in a reflexive Banach space from its finite samples as an optimization problem. Within the framework of reproducing kernel Banach spaces, we prove the representer theorem for the minimizer of regularized learning schemes with a general loss function and a nondecreasing regularizer. When the loss function and the regularizer are differentiable, a characterization equation for the minimizer is also established. Our techniques include the use of generalized duality mapping between a vector space and its dual, and the induced semi-inner product operation as generalizing the inner product operator of the (self-dual) Hilbert spaces.