Optimal Estimates for Pairwise Learning with Deep ReLU Networks

05/31/2023

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by   Junyu Zhou, et al.

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Pairwise learning refers to learning tasks where a loss takes a pair of samples into consideration. In this paper, we study pairwise learning with deep ReLU networks and estimate the excess generalization error. For a general loss satisfying some mild conditions, a sharp bound for the estimation error of order O((Vlog(n) /n)^1/(2-β)) is established. In particular, with the pairwise least squares loss, we derive a nearly optimal bound of the excess generalization error which achieves the minimax lower bound up to a logrithmic term when the true predictor satisfies some smoothness regularities.