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Decision-focused learning (DFL) was recently proposed for stochasticoptimization problems that involve unknown parameters. By integratingpredictive modeling with an implicitly differentiable optimization layer, DFLhas shown superior performance to the standard two-stage predict-then-optimizepipeline. However, most existing DFL methods are only applicable to convexproblems or a subset of nonconvex problems that can be easily relaxed to convexones. Further, they can be inefficient in training due to the requirement ofsolving and differentiating through the optimization problem in every trainingiteration. We propose SO-EBM, a general and efficient DFL method for stochasticoptimization using energy-based models. Instead of relying on KKT conditions toinduce an implicit optimization layer, SO-EBM explicitly parameterizes theoriginal optimization problem using a differentiable optimization layer basedon energy functions. To better approximate the optimization landscape, wepropose a coupled training objective that uses a maximum likelihood loss tocapture the optimum location and a distribution-based regularizer to capturethe overall energy landscape. Finally, we propose an efficient trainingprocedure for SO-EBM with a self-normalized importance sampler based on aGaussian mixture proposal. We evaluate SO-EBM in three applications: powerscheduling, COVID-19 resource allocation, and non-convex adversarial securitygame, demonstrating the effectiveness and efficiency of SO-EBM.

End-to-End Stochastic Optimization with Energy-Based Model