For the past couple of decades, numerical optimization has played a centralrole in addressing wireless resource management problems such as power controland beamformer design. However, optimization algorithms often entailconsiderable complexity, which creates a serious gap between theoreticaldesign/analysis and real-time processing. To address this challenge, we proposea new learning-based approach. The key idea is to treat the input and output ofa resource allocation algorithm as an unknown non-linear mapping and use a deepneural network (DNN) to approximate it. If the non-linear mapping can belearned accurately by a DNN of moderate size, then resource allocation can bedone in almost real time -- since passing the input through a DNN only requiresa small number of simple operations. In this work, we address both the thereotical and practical aspects ofDNN-based algorithm approximation with applications to wireless resourcemanagement. We first pin down a class of optimization algorithms that are`learnable' in theory by a fully connected DNN. Then, we focus on DNN-basedapproximation to a popular power allocation algorithm named WMMSE (Shi {\it etal} 2011). We show that using a DNN to approximate WMMSE can be fairly accurate-- the approximation error $\epsilon$ depends mildly [in the order of$\log(1/\epsilon)$] on the numbers of neurons and layers of the DNN. On theimplementation side, we use extensive numerical simulations to demonstrate thatDNNs can achieve orders of magnitude speedup in computational time compared tostate-of-the-art power allocation algorithms based on optimization.
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