  Many important multiple-objective decision problems can be cast within the
framework of ranking under constraints and solved via a weighted bipartite
matching linear program. Some of these optimization problems, such as
personalized content recommendations, may need to be solved in real time and
thus must comply with strict time requirements to prevent the perception of
latency by consumers. Classical linear programming is too computationally
inefficient for such settings. We propose a novel approach to scale up ranking
under constraints by replacing the weighted bipartite matching optimization
with a prediction problem in the algorithm deployment stage. We show
empirically that the proposed approximate solution to the ranking problem leads
to a major reduction in required computing resources without much sacrifice in
constraint compliance and achieved utility, allowing us to solve larger
constrained ranking problems real-time, within the required 50 milliseconds,
than previously reported.
