A gradient step is then made to optimize the pairwise hinge loss: We use m = 0.1 in our experiments.
this loss function is referred to as the WARP loss in  and is used to approximately optimizing the top of the ranked list, useful for metrics like precision and recall@k. the search for a negative candidate tag means that more energy is spent on improving the ranking performance of positive labels already near the top of the ranked list, compared to only randomly sampling of negatives, which would optimize the average rank instead.