  Decision-focused learning (DFL) was recently proposed for stochastic
optimization problems that involve unknown parameters. By integrating
predictive modeling with an implicitly differentiable optimization layer, DFL
has shown superior performance to the standard two-stage predict-then-optimize
pipeline. However, most existing DFL methods are only applicable to convex
problems or a subset of nonconvex problems that can be easily relaxed to convex
ones. Further, they can be inefficient in training due to the requirement of
solving and differentiating through the optimization problem in every training
iteration. We propose SO-EBM, a general and efficient DFL method for stochastic
optimization using energy-based models. Instead of relying on KKT conditions to
induce an implicit optimization layer, SO-EBM explicitly parameterizes the
original optimization problem using a differentiable optimization layer based
on energy functions. To better approximate the optimization landscape, we
propose a coupled training objective that uses a maximum likelihood loss to
capture the optimum location and a distribution-based regularizer to capture
the overall energy landscape. Finally, we propose an efficient training
procedure for SO-EBM with a self-normalized importance sampler based on a
Gaussian mixture proposal. We evaluate SO-EBM in three applications: power
scheduling, COVID-19 resource allocation, and non-convex adversarial security
game, demonstrating the effectiveness and efficiency of SO-EBM.
