Penalty-Based multitask estimation with non-local linear equality constraints

Abstract

We consider distributed estimation problems over multitask networks where the parameter vectors at distinct agents are coupled via a set of linear equality constraints. Unlike previous existing works, the current work assumes that each constraint involves agents that are not necessarily one-hop neighbors. At each time instant, we assume that each agent has access to the instantaneous estimates of its one-hop neighbors and to the past estimates of its multi-hop neighbors through a multi-hop relay protocol. A distributed penalty-based algorithm is then derived and its performance analyses in the mean and in the mean-square-error sense are provided. Simulation results show the effectiveness of the strategy and validate the theoretical models.