In important applications involving multi-task networks with multiple objectives, agents in the network need to decide between these multiple objectives and reach an agreement about which single objective to follow for the network. In this work we propose a distributed decision-making algorithm. The agents are assumed to observe data that may be generated by different models. Through localized interactions, the agents reach agreement about which model to track and interact with each other in order to enhance the network performance. We investigate the approach for both static and mobile networks. The simulations illustrate the performance of the proposed strategies.
We consider a distributed mean-square-error estimation problem over an @math -agent network. The connectivity of the agents is described by a graph (see Fig. ). Data sensed by any particular agent can arise from one of different models. The objective is to reach an agreement among all agents in the network on one common model to estimate. Two definitions are introduced: the observed model, which refers to the model from which an agent collects data, and the desired model, which refers to the model the agent decides to estimate. The agents do not know which model generated the data they collect; they also do not know which other agents in their neighborhood sense data arising from the same model. Therefore, each agent needs to determine the subset of its neighbors that observes the same model. This initial step is referred to as clustering . Since the decision-making objective depends on the clustering output, errors made during the clustering process have an impact on the global decision. In this work, we rely on the clustering technique proposed in @cite_2 to reduce this effect.
@cite_2
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We consider the problem of decentralized clustering and estimation over multitask networks, where agents infer and track different models of interest. The agents do not know beforehand which model is generating their own data. They also do not know which agents in their neighborhood belong to the same cluster. We propose a decentralized clustering algorithm aimed at identifying and forming clusters of agents of similar objectives, and at guiding cooperation to enhance the inference performance. One key feature of the proposed technique is the integration of the learning and clustering tasks into a single strategy. We analyze the performance of the procedure and show that the error probabilities of types I and II decay exponentially to zero with the step-size parameter. While links between agents following different objectives are ignored in the clustering process, we nevertheless show how to exploit these links to relay critical information across the network for enhanced performance. Simulation results illustrate the performance of the proposed method in comparison to other useful techniques.