  Solving optimization problems is the key to decision making in many real-life
analytics applications. However, the coefficients of the optimization problems
are often uncertain and dependent on external factors, such as future demand or
energy or stock prices. Machine learning (ML) models, especially neural
networks, are increasingly being used to estimate these coefficients in a
data-driven way. Hence, end-to-end predict-and-optimize approaches, which
consider how effective the predicted values are to solve the optimization
problem, have received increasing attention. In case of integer linear
programming problems, a popular approach to overcome their non-differentiabilty
is to add a quadratic penalty term to the continuous relaxation, such that
results from differentiating over quadratic programs can be used. Instead we
investigate the use of the more principled logarithmic barrier term, as widely
used in interior point solvers for linear programming. Specifically, instead of
differentiating the KKT conditions, we consider the homogeneous self-dual
formulation of the LP and we show the relation between the interior point step
direction and corresponding gradients needed for learning. Finally our
empirical experiments demonstrate our approach performs as good as if not
better than the state-of-the-art QPTL (Quadratic Programming task loss)
formulation of Wilder et al. and SPO approach of Elmachtoub and Grigas.
