Score Function Gradient Estimation to Widen the Applicability of
  Decision-Focused Learning
Mattia Silvestri Senne Berden Jayanta Mandi Ali İrfan Mahmutoğulları Maxime Mulamba Allegra De Filippo Tias Guns Michele Lombardi
Many real-world optimization problems contain unknown parameters that must be
predicted prior to solving. To train the predictive machine learning (ML)
models involved, the commonly adopted approach focuses on maximizing predictive
accuracy. However, this approach does not always lead to the minimization of
the downstream task loss. Decision-focused learning (DFL) is a recently
proposed paradigm whose goal is to train the ML model by directly minimizing
the task loss. However, state-of-the-art DFL methods are limited by the
assumptions they make about the structure of the optimization problem (e.g.,
that the problem is linear) and by the fact that can only predict parameters
that appear in the objective function. In this work, we address these
limitations by instead predicting \textit{distributions} over parameters and
adopting score function gradient estimation (SFGE) to compute decision-focused
updates to the predictive model, thereby widening the applicability of DFL. Our
experiments show that by using SFGE we can: (1) deal with predictions that
occur both in the objective function and in the constraints; and (2)
effectively tackle two-stage stochastic optimization problems.