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In this paper, the authors explain about the asynchronous behavior of diffusion adaptation strategies for distributed optimization over networks. Under the assumed model, agents in the network may stop updating their estimates or may stop exchanging information at random times. It is expected that asynchronous behavior degrades performance. The analysis quantifies by how much performance degrades and reveals that the learning rate and the mean-square stability conditions of the network are influenced by the rates of occurrence of the asynchronous events.
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