  Machine learning has become successful in solving wireless interference
management problems. Different kinds of deep neural networks (DNNs) have been
trained to accomplish key tasks such as power control, beamforming and
admission control. There are two popular training paradigms for such DNNs-based
interference management models: supervised learning (i.e., fitting labels
generated by an optimization algorithm) and unsupervised learning (i.e.,
directly optimizing some system performance measure). Although both of these
paradigms have been extensively applied in practice, due to the lack of any
theoretical understanding about these methods, it is not clear how to
systematically understand and compare their performance.
  In this work, we conduct theoretical studies to provide some in-depth
understanding about these two training paradigms. First, we show a somewhat
surprising result, that for some special power control problem, the
unsupervised learning can perform much worse than its supervised counterpart,
because it is more likely to stuck at some low-quality local solutions. We then
provide a series of theoretical results to further understand the properties of
the two approaches. Generally speaking, we show that when high-quality labels
are available, then the supervised learning is less likely to be stuck at a
solution than its unsupervised counterpart. Additionally, we develop a
semi-supervised learning approach which properly integrates these two training
paradigms, and can effectively utilize limited number of labels to find
high-quality solutions. To our knowledge, these are the first set of
theoretical results trying to understand different training approaches in
learning-based wireless communication system design.
