  Deep neural networks (DNNs) have been introduced for designing wireless
policies by approximating the mappings from environmental parameters to
solutions of optimization problems. Considering that labeled training samples
are hard to obtain, unsupervised deep learning has been proposed to solve
functional optimization problems with statistical constraints recently.
However, most existing problems in wireless communications are variable
optimizations, and many problems are with instantaneous constraints. In this
paper, we establish a unified framework of using unsupervised deep learning to
solve both kinds of problems with both instantaneous and statistic constraints.
For a constrained variable optimization, we first convert it into an equivalent
functional optimization problem with instantaneous constraints. Then, to ensure
the instantaneous constraints in the functional optimization problems, we use
DNN to approximate the Lagrange multiplier functions, which is trained together
with a DNN to approximate the policy. We take two resource allocation problems
in ultra-reliable and low-latency communications as examples to illustrate how
to guarantee the complex and stringent quality-of-service (QoS) constraints
with the framework. Simulation results show that unsupervised learning
outperforms supervised learning in terms of QoS violation probability and
approximation accuracy of the optimal policy, and can converge rapidly with
pre-training.
