Unsupervised Learning for Parametric Optimization

This letter proposes the unsupervised training of a feedforward neural network to solve parametric optimization problems involving large numbers of parameters. Such unsupervised training, which consists in repeatedly sampling parameter values and performing stochastic gradient descent, foregoes the taxing precomputation of labeled training data that supervised learning necessitates. As an example of application, we put this technique to use on a rather general constrained quadratic program. Follow-up letters subsequently apply it to more specialized wireless communication problems, some of them nonconvex in nature. In all cases, the performance of the proposed procedure is very satisfactory and, in terms of computational cost, its scalability with the problem dimensionality is superior to that of convex solvers.