Deep Neural Network-Based Algorithm Approximation via Multivariate Polynomial Regression

Many communication tasks have been formulated as optimization problems that can be solved by iterative algorithms. However, these algorithms are usually computationally intensive. To enable real-time processing of communication algorithms, in this paper, we propose a new deep neural network (DNN) architecture for algorithm approximation. Based on the idea of deep unfolding, we expand the iterative algorithm into a cascade network structure of basic blocks, with each network block corresponding to an iteration. Then, instead of directly approximating each iteration through network layers, we introduce the multivariate polynomial regression (MPR) as a bridge between the iterations and layers for constructing the unfolded network blocks. Specifically, we use a multivariate polynomial to approximate an iteration of the original iterative algorithm, and further construct a shallow neural network with one hidden layer to realize the polynomial, where the order of the polynomial provides theoretical guidance for determining the size of the network and controls the tradeoff between the approximation accuracy and computation speed. As empirical justifications, we apply the proposed DNN architecture in approximating the classic WMMSE algorithm for wireless interference management, showing that the proposed approach can achieve a good approximation accuracy with a much faster computation speed.