Decentralized Multitask Recursive Least Squares with Local Linear Constraints

In this paper, we study decentralized multitask recursive least squares, where each node in a network has an unknown weight vector to estimate. The weight vectors of neigh-boring nodes are related through local linear equality constraints, e.g., the flow conservation constraints in network flow control. We propose a modified dual gradient ascent algorithm, which is both decentralized and online. The mean square convergence of the algorithm is established under standard assumptions. It is shown that both the mean square deviation and the excess mean square error converge to zero at geometric rates.