  This paper presents a machine learning strategy that tackles a distributed
optimization task in a wireless network with an arbitrary number of randomly
interconnected nodes. Individual nodes decide their optimal states with
distributed coordination among other nodes through randomly varying backhaul
links. This poses a technical challenge in distributed universal optimization
policy robust to a random topology of the wireless network, which has not been
properly addressed by conventional deep neural networks (DNNs) with rigid
structural configurations. We develop a flexible DNN formalism termed
distributed message-passing neural network (DMPNN) with forward and backward
computations independent of the network topology. A key enabler of this
approach is an iterative message-sharing strategy through arbitrarily connected
backhaul links. The DMPNN provides a convergent solution for iterative
coordination by learning numerous random backhaul interactions. The DMPNN is
investigated for various configurations of the power control in wireless
networks, and intensive numerical results prove its universality and viability
over conventional optimization and DNN approaches.
