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 $O((V\log(n) /n)^{1/(2-\beta)})$ 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.

翻译：成对学习是指损失函数考虑样本对的学习任务。本文研究基于深度ReLU网络的成对学习，并估计其超额泛化误差。对于满足某些温和条件的一般损失函数，我们建立了阶数为$O((V\log(n) /n)^{1/(2-\beta)})$的估计误差的锐界。特别地，在成对最小二乘损失下，当真实预测器满足某些光滑性正则条件时，我们导出了超额泛化误差的近乎最优界，该界在对数项范围内达到了极小化最优下界。