Triplet learning, i.e. learning from triplet data, has attracted much attention in computer vision tasks with an extremely large number of categories, e.g., face recognition and person re-identification. Albeit with rapid progress in designing and applying triplet learning algorithms, there is a lacking study on the theoretical understanding of their generalization performance. To fill this gap, this paper investigates the generalization guarantees of triplet learning by leveraging the stability analysis. Specifically, we establish the first general high-probability generalization bound for the triplet learning algorithm satisfying the uniform stability, and then obtain the excess risk bounds of the order $O(n^{-\frac{1}{2}} \mathrm{log}n)$ for both stochastic gradient descent (SGD) and regularized risk minimization (RRM), where $2n$ is approximately equal to the number of training samples. Moreover, an optimistic generalization bound in expectation as fast as $O(n^{-1})$ is derived for RRM in a low noise case via the on-average stability analysis. Finally, our results are applied to triplet metric learning to characterize its theoretical underpinning.

翻译：三元组学习，即从三元组数据中进行学习，在类别数量极大的计算机视觉任务中引起了广泛关注，例如人脸识别和行人重识别。尽管三元组学习算法的设计和应用取得了快速进展，但其泛化性能的理论理解仍缺乏研究。为填补这一空白，本文通过稳定性分析探讨三元组学习的泛化保证。具体而言，我们首次建立了满足均匀稳定性的三元组学习算法的一般高概率泛化界，进而针对随机梯度下降（SGD）和正则化风险最小化（RRM）分别得到了阶为$O(n^{-\frac{1}{2}} \mathrm{log}n)$的过余风险界，其中$2n$近似等于训练样本数量。此外，通过平均稳定性分析，在低噪声情形下，我们为RRM导出了期望中快至$O(n^{-1})$的乐观泛化界。最后，我们将所得结果应用于三元组度量学习，以刻画其理论基础。