Stochastic Submodular Maximization for Scalable Network Adaptation in Dense Cloud-RAN

We propose a stochastic submodular maximization approach to enable scalable network adaptation in dense cloud radio access networks (Cloud-RAN) without any prior knowledge of the underlying channel distribution. This is achieved by exploiting the submodular and monotone characteristics of the objective function, followed by equivalently lifting the discrete problem into the continuous domain via multilinear extension. Although maximizing the continuous submodular function is still nonconvex, the stochastic projected gradient method is able to provide strong approximation guarantees to the global maxima. As the channel distribution is unknown, we propose to access the unbiased estimate of gradient only based on the historically collected channel samples, thereby significantly reducing the channel signaling overhead. We further provide a fast way to compute the unbiased estimate of gradient by exploiting the algebraic structure in the continuous submodular function. Therefore, the proposed stochastic submodular maximization based network adaptation framework enjoys the benefits of low computational complexity and low channel signaling overhead. Simulation results demonstrate the algorithmic advantages and desirable performances of the proposed methods for network adaptation in dense Cloud-RAN.