Convergence Bounds for Federated Learning for Linear Regression Model Tuning in Communication Systems

Linear regression models are increasingly becoming important in communication system operational efficiency improvement with applications in prediction-based demodulation in Non Orthogonal Multiple Access (NOMA) systems like LoRa, UE trajectory prediction in new 3GPP work/study items, environmental observation in edge computing systems, etc. We analyze the convergence dynamics of linear regression problems in a federated learning environment. The learning rate is an important control parameter when considering the convergence of the system. Thus, we give results which relate the learning rate to the convergence time and find probabilities with which the setup diverges for a given learning rate. We also study the convergence of the setup when devices participate in the learning in a probabilistic manner to account for communication breakdowns, device inactivity or even when the communication resources are constrained. This leads to a study of the trade-off between computation and convergence. We also look at a method which can be used to make the system converge in 2 iterations thus saving on computation and communication resources.