  The core objective of modelling recommender systems from implicit feedback is
to maximize the positive sample score $s_p$ and minimize the negative sample
score $s_n$, which can usually be summarized into two paradigms: the pointwise
and the pairwise. The pointwise approaches fit each sample with its label
individually, which is flexible in weighting and sampling on instance-level but
ignores the inherent ranking property. By qualitatively minimizing the relative
score $s_n - s_p$, the pairwise approaches capture the ranking of samples
naturally but suffer from training efficiency. Additionally, both approaches
are hard to explicitly provide a personalized decision boundary to determine if
users are interested in items unseen. To address those issues, we innovatively
introduce an auxiliary score $b_u$ for each user to represent the User Interest
Boundary(UIB) and individually penalize samples that cross the boundary with
pairwise paradigms, i.e., the positive samples whose score is lower than $b_u$
and the negative samples whose score is higher than $b_u$. In this way, our
approach successfully achieves a hybrid loss of the pointwise and the pairwise
to combine the advantages of both. Analytically, we show that our approach can
provide a personalized decision boundary and significantly improve the training
efficiency without any special sampling strategy. Extensive results show that
our approach achieves significant improvements on not only the classical
pointwise or pairwise models but also state-of-the-art models with complex loss
function and complicated feature encoding.
