Distributed Online Learning Over Multitask Networks With Rank-One Model

Modeling multitask relations in distributed networks has garnered considerable interest in recent years. In this paper, we present a novel rank-one model, where all the optimal vectors to be estimated are scaled versions of an unknown vector to be determined. By considering the rank-one relation, we develop a constrained centralized optimization problem, and after a decoupling process, it is solved in a distributed way by using the projected gradient descent method. To perform an efficient calculation of this projection, we suggest substituting the intensive singular value decomposition with the computationally efficient power method. Additionally, local estimates targeting the same optimal vector are combined within a neighborhood to further improve their accuracy. Theoretical analyses of the proposed algorithm are conducted for star topologies, and conditions are derived to guarantee its stability in both the mean and mean-square senses. Finally, simulation results are presented to demonstrate the effectiveness of the proposed algorithms.