Two-Stage Predict+Optimize for Mixed Integer Linear Programs with
  Unknown Parameters in Constraints
Xinyi Hu Jasper C. H. Lee Jimmy H. M. Lee
Consider the setting of constrained optimization, with some parameters
unknown at solving time and requiring prediction from relevant features.
Predict+Optimize is a recent framework for end-to-end training supervised
learning models for such predictions, incorporating information about the
optimization problem in the training process in order to yield better
predictions in terms of the quality of the predicted solution under the true
parameters. Almost all prior works have focused on the special case where the
unknowns appear only in the optimization objective and not the constraints. Hu
et al.~proposed the first adaptation of Predict+Optimize to handle unknowns
appearing in constraints, but the framework has somewhat ad-hoc elements, and
they provided a training algorithm only for covering and packing linear
programs. In this work, we give a new \emph{simpler} and \emph{more powerful}
framework called \emph{Two-Stage Predict+Optimize}, which we believe should be
the canonical framework for the Predict+Optimize setting. We also give a
training algorithm usable for all mixed integer linear programs, vastly
generalizing the applicability of the framework. Experimental results
demonstrate the superior prediction performance of our training framework over
all classical and state-of-the-art methods.