Machine Learning Meets Stochastic Geometry: Determinantal Subset Selection for Wireless Networks

In wireless networks, many problems can be formulated as subset selection problems where the goal is to select a subset from the ground set with the objective of maximizing some objective function. These problems are typically NP-hard and hence solved through carefully constructed heuristics, which are themselves mostly NP-complete and thus not easily applicable to large networks. On the other hand, subset selection problems occur in slightly different context in machine learning (ML) where the goal is to select a subset of high quality yet diverse items from a ground set. This balance in quality and diversity is often maintained in the ML problems by using determinantal point process (DPP), which endows distributions on the subsets such that the probability of selecting two similar items is negatively correlated. While DPPs have been explored more generally in stochastic geometry (SG) to model inter-point repulsion, they are particularly conducive for ML applications because the parameters of their distributions can be efficiently learnt from a training set. In this paper, we introduce a novel DPP-based learning (DPPL) framework for efficiently solving subset selection problems in wireless networks. The DPPL is intended to replace the traditional optimization algorithms for subset selection by learning the quality-diversity trade-off in the optimal subsets selected by an optimization routine. As a case study, we apply DPPL to the wireless link scheduling problem, where the goal is to determine the subset of simultaneously active links which maximizes the network-wide sum-rate. We demonstrate that the proposed DPPL approaches the optimal solution with significantly lower computational complexity than the popular optimization algorithms used for this problem in the literature.