On the Learnability of Multilabel Ranking

Multilabel ranking is a central task in machine learning with widespread applications to web search, news stories, recommender systems, etc. However, the most fundamental question of learnability in a multilabel ranking setting remains unanswered. In this paper, we characterize the learnability of multilabel ranking problems in both the batch and online settings for a large family of ranking losses. Along the way, we also give the first equivalence class of ranking losses based on learnability.