It is known that more and more mathematicians have paid their attention to the field of learning with a Banach space since Banach spaces may provide abundant inner-product structures. We give investigations on the convergence of a kernel-regularized online binary classification learning algorithm in the setting of reproducing kernel Banach spaces (RKBSs), design an online iteration algorithm with the subdifferential of the norm and the logistic loss, and provide an upper bound for the learning rate, which shows that the online learning algorithm converges if RKBSs satisfy 2-uniform convexity.

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