Predict-Then-Optimize by Proxy: Learning Joint Models of Prediction and
  Optimization
James Kotary Vincenzo Di Vito Jacob Christopher Pascal Van Hentenryck Ferdinando Fioretto
Many real-world decision processes are modeled by optimization problems whose
defining parameters are unknown and must be inferred from observable data. The
Predict-Then-Optimize framework uses machine learning models to predict unknown
parameters of an optimization problem from features before solving. Recent
works show that decision quality can be improved in this setting by solving and
differentiating the optimization problem in the training loop, enabling
end-to-end training with loss functions defined directly on the resulting
decisions. However, this approach can be inefficient and requires handcrafted,
problem-specific rules for backpropagation through the optimization step. This
paper proposes an alternative method, in which optimal solutions are learned
directly from the observable features by predictive models. The approach is
generic, and based on an adaptation of the Learning-to-Optimize paradigm, from
which a rich variety of existing techniques can be employed. Experimental
evaluations show the ability of several Learning-to-Optimize methods to provide
efficient, accurate, and flexible solutions to an array of challenging
Predict-Then-Optimize problems.