  Embedding models, which learn latent representations of users and items based
on user-item interaction patterns, are a key component of recommendation
systems. In many applications, contextual constraints need to be applied to
refine recommendations, e.g. when a user specifies a price range or product
category filter. The conventional approach, for both context-aware and standard
models, is to retrieve items and apply the constraints as independent
operations. The order in which these two steps are executed can induce
significant problems. For example, applying constraints a posteriori can result
in incomplete recommendations or low-quality results for the tail of the
distribution (i.e., less popular items). As a result, the additional
information that the constraint brings about user intent may not be accurately
captured.
  In this paper we propose integrating the information provided by the
contextual constraint into the similarity computation, by merging constraint
application and retrieval into one operation in the embedding space. This
technique allows us to generate high-quality recommendations for the specified
constraint. Our approach learns constraints representations jointly with the
user and item embeddings. We incorporate our methods into a matrix
factorization model, and perform an experimental evaluation on one internal and
two real-world datasets. Our results show significant improvements in
predictive performance compared to context-aware and standard models.
