Dual Domain Learning of Optimal Resource Allocations in Wireless Systems

We consider the problem of finding optimal resource allocations subject to system constraints in a generic class of problems in wireless communications. These problems are inherently challenging due to functional optimization and potential non-convexities. However, these problems can be observed to take the form of a regression problem, although one in which the statistical loss function appears as a constraint. This motivates the use of machine learning model parameterizations. To apply gradient-based solution algorithms that do not require model knowledge, we convert the constrained optimization problem to an unconstrained one using Lagrangian duality. Despite the non-convexity in the problem, we formally show that the sub-optimality of the dual domain problem is small when the learning parameterization is sufficiently dense. We then present a primal-dual learning algorithm that looks for solutions to the dual problem using model-free gradient estimates. In a numerical simulation, we demonstrate the near-optimality of the proposed model-free algorithm using a neural network parametrization for a capacity maximization problem.