  This paper considers the design of optimal resource allocation policies in
wireless communication systems which are generically modeled as a functional
optimization problem with stochastic constraints. These optimization problems
have the structure of a learning problem in which the statistical loss appears
as a constraint, motivating the development of learning methodologies to
attempt their solution. To handle stochastic constraints, training is
undertaken in the dual domain. It is shown that this can be done with small
loss of optimality when using near-universal learning parameterizations. In
particular, since deep neural networks (DNN) are near-universal their use is
advocated and explored. DNNs are trained here with a model-free primal-dual
method that simultaneously learns a DNN parametrization of the resource
allocation policy and optimizes the primal and dual variables. Numerical
simulations demonstrate the strong performance of the proposed approach on a
number of common wireless resource allocation problems.
