Abstract: Most popular metric learning losses have no direct relation with the evaluation metrics that are subsequently applied to evaluate their performance. We hypothesize that training a metric learning model by maximizing the area under the ROC curve (which is a typical performance measure of recognition systems) can induce an implicit ranking suitable for retrieval problems. This hypothesis is supported by previous work that proved that a curve dominates in ROC space if and only if it dominates in Precision-Recall space. To test this hypothesis, we design and maximize an approximated, derivable relaxation of the area under the ROC curve. The proposed AUC loss achieves state-of-the-art results on two large scale retrieval benchmark datasets (Stanford Online Products and DeepFashion In-Shop). Moreover, the AUC loss achieves comparable performance to more complex, domain specific, state-of-the-art methods for vehicle re-identification.