Differentiable Ranking Metric Using Relaxed Sorting for Top-K Recommendation

Most recommenders generate recommendations for a user by computing the preference score of items, sorting the items according to the score, and filtering top-
$K$
-items of high scores. Since sorting is not differentiable and is difficult to optimize with gradient descent, it is nontrivial to incorporate it in recommendation model training despite its relevance to top-
$K$
recommendations. As a result, inconsistency occurs between existing learning objectives and ranking metrics of recommenders. In this work, we present the Differentiable Ranking Metric (DRM) that mitigates the inconsistency between model training and generating top-
$K$
recommendations, aiming at improving recommendation performance by employing the differentiable relaxation of ranking metrics via joint learning. Using experiments with several real-world datasets, we demonstrate that the joint learning of the DRM objective and existing factor based recommenders significantly improves the quality of recommendations.