  Dealing with uncertainty in optimization parameters is an important and
longstanding challenge. Typically, uncertain parameters are predicted
accurately, and then a deterministic optimization problem is solved. However,
the decisions produced by this so-called \emph{predict-then-optimize} procedure
can be highly sensitive to uncertain parameters. In this work, we contribute to
recent efforts in producing \emph{decision-focused} predictions, i.e., to build
predictive models that are constructed with the goal of minimizing a
\emph{regret} measure on the decisions taken with them. We formulate the exact
expected regret minimization as a pessimistic bilevel optimization model. Then,
using duality arguments, we reformulate it as a non-convex quadratic
optimization problem. Finally, we show various computational techniques to
achieve tractability. We report extensive computational results on
shortest-path instances with uncertain cost vectors. Our results indicate that
our approach can improve training performance over the approach of Elmachtoub
and Grigas (2022), a state-of-the-art method for decision-focused learning.

Machine Learning;Optimization and Control