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A Lagrangian Dual Framework for Deep Neural Networks with Constraints

A variety of computationally challenging constrained optimization problems in several engineering disciplines are solved repeatedly under different scenarios. In many cases, they would benefit from fast and accurate approximations, either to support real-time operations or large-scale simulation studies. This paper aims at exploring how to leverage the substantial data being accumulated by repeatedly solving instances of these applications over time. It introduces a deep learning model that exploits Lagrangian duality to encourage the satisfaction of hard constraints. The proposed method is evaluated on a collection of realistic energy networks, by enforcing non-discriminatory decisions on a variety of datasets, and on a transprecision computing application. The results illustrate the effectiveness of the proposed method that dramatically decreases constraint violations by the predictors and, in some applications, increases the prediction accuracy.