  In this paper, we investigate the recommendation task in the most common
scenario with implicit feedback (e.g., clicks, purchases). State-of-the-art
methods in this direction usually cast the problem as to learn a personalized
ranking on a set of items (e.g., webpages, products). The top-N results are
then provided to users as recommendations, where the N is usually a fixed
number pre-defined by the system according to some heuristic criteria (e.g.,
page size, screen size). There is one major assumption underlying this
fixed-number recommendation scheme, i.e., there are always sufficient relevant
items to users' preferences. Unfortunately, this assumption may not always hold
in real-world scenarios. In some applications, there might be very limited
candidate items to recommend, and some users may have very high relevance
requirement in recommendation. In this way, even the top-1 ranked item may not
be relevant to a user's preference. Therefore, we argue that it is critical to
provide a dynamic-K recommendation, where the K should be different with
respect to the candidate item set and the target user. We formulate this
dynamic-K recommendation task as a joint learning problem with both ranking and
classification objectives. The ranking objective is the same as existing
methods, i.e., to create a ranking list of items according to users' interests.
The classification objective is unique in this work, which aims to learn a
personalized decision boundary to differentiate the relevant items from
irrelevant items. Based on these ideas, we extend two state-of-the-art
ranking-based recommendation methods, i.e., BPRMF and HRM, to the corresponding
dynamic-K versions, namely DK-BPRMF and DK-HRM. Our experimental results on two
datasets show that the dynamic-K models are more effective than the original
fixed-N recommendation methods.
