  Machine learning components commonly appear in larger decision-making
pipelines; however, the model training process typically focuses only on a loss
that measures accuracy between predicted values and ground truth values.
Decision-focused learning explicitly integrates the downstream decision problem
when training the predictive model, in order to optimize the quality of
decisions induced by the predictions. It has been successfully applied to
several limited combinatorial problem classes, such as those that can be
expressed as linear programs (LP), and submodular optimization. However, these
previous applications have uniformly focused on problems from specific classes
with simple constraints. Here, we enable decision-focused learning for the
broad class of problems that can be encoded as a Mixed Integer Linear Program
(MIP), hence supporting arbitrary linear constraints over discrete and
continuous variables. We show how to differentiate through a MIP by employing a
cutting planes solution approach, which is an exact algorithm that iteratively
adds constraints to a continuous relaxation of the problem until an integral
solution is found. We evaluate our new end-to-end approach on several real
world domains and show that it outperforms the standard two phase approaches
that treat prediction and prescription separately, as well as a baseline
approach of simply applying decision-focused learning to the LP relaxation of
the MIP.
