Transformer Based Approach for Wireless Resource Allocation Problems Involving Mixed Discrete and Continuous Variables

Many challenging wireless communication problems involve jointly optimizing a set of discrete variables (e.g., subset of antennas) and continuous variables (e.g., power allocation), where the subproblem involving discrete variables are intrinsically combinatorial. Although many heuristic methods have been developed to deal with these problems (e.g., greedy based, exhaustive search based methods), they still incur high computational costs. In this work, we propose a machine learning-based algorithm to learn an approximate high-quality solution for this class of problems. Differently than the existing learning-based methods which mostly only focusing on continuous problems, we propose a two-stage approach, where in the first stage a Transformer is used to find the set of discrete variables, followed by a second stage where the continuous variables are optimized (while fixing the dicrete variables). We demonstrate the effectiveness of our approach using a joint user scheduling and beamforming problem in MIMO systems. We show that the proposed method can generate high-quality active user sets, even with low-quality channel state information, while only using a fraction of computational time compared with a heuristic greedy algorithm.