Online Parameter Estimation Over Distributed Multitask Networks with a Rank-One Model

In recent years, modeling multitask relations in distributed networks has garnered considerable attention. Motivated by various practical applications, we propose a novel distributed multitask network model, termed the rank-one model, where each optimum vector to be estimated is a scaled representation of the others. To address the optimization problem with the rank-one constraint in a distributed manner, it is crucial to decouple the variables within the constraint, achieved by locally relaxing it at each node. Subsequently, local constrained distributed optimization problems are resolved using the projected gradient descent method, with the added challenge of projecting onto a non-convex rank-one space. Efficient evaluation of this projection is achieved using the computationally efficient power method. Additionally, theoretical analyses are performed on the proposed algorithm, particularly focusing on a special case of star topologies, with provided conditions ensuring stability in both the mean and mean-square senses. Finally, simulation results are presented to demonstrate the effectiveness of the proposed algorithm.