Performance of the Bayesian Online Algorithm for the Perceptron

In this letter, we derive continuum equations for the generalization error of the Bayesian online algorithm (BOnA) for the one-layer perceptron with a spherical covariance matrix using the Rosenblatt potential and show, by numerical calculations, that the asymptotic performance of the algorithm is the same as the one for the optimal algorithm found by means of variational methods with the added advantage that the BOnA does not use any inaccessible information during learning