Pairwise learning naturally arises from machine learning tasks such as AUC maximization, ranking, and metric learning. In this paper we propose a new pairwise learning algorithm based on the additive noise regression model, which adopts the pairwise Huber loss and applies effectively even to the situation where the noise only satisfies a weak moment condition. Owing to the robustness of Huber loss function, this new method is resistant to heavy-tailed errors or outliers in the response variable. We establish a comparison theorem to characterize the gap between the excess generalization error and the prediction error. We derive the error bounds and convergence rates under appropriate conditions. It is worth mentioning that all the results are established under the $(1+ϵ)$-th moment condition of the noise variable. It is rather weak particularly in the case of $ϵ<1$, which means the noise variable does not even admit a finite variance.

成对学习自然产生于机器学习任务，例如 AUC 最大化、排名和度量学习。在本文中，我们提出了一种新的基于加性噪声回归模型的成对学习算法，该算法采用成对 Huber 损失，即使在噪声仅满足弱矩条件的情况下也能有效应用。由于 Huber 损失函数的稳健性，这种新方法可以抵抗响应变量中的重尾误差或异常值。我们建立了一个比较定理来表征过度泛化误差和预测误差之间的差距。我们推导出适当条件下的误差界限和收敛速度。值得一提的是，所有的结果都建立在$(1+\epsilon )$- 噪声变量的时刻条件。它是相当弱的，尤其是在$\epsilon <1$，这意味着噪声变量甚至不允许有限方差。