Penalty-based multitask distributed adaptation over networks with constraints

Multitask distributed optimization over networks enables the agents to cooperate locally to estimate multiple related parameter vectors. In this work, we consider multitask estimation problems over mean-square-error (MSE) networks where each agent is interested in estimating its own parameter vector, also called task, and where the tasks are related according to a set of linear equality constraints. We assume that each agent possesses its own cost and that the set of constraints is distributed among the agents. In order to solve the multitask problem, a cooperative algorithm based on penalty method is derived. Some results on its stability and convergence properties are also provided. Simulations are conducted to illustrate the theoretical results and show the efficiency of the strategy.