Chapter 1 - Asynchronous Adaptive Networks

Abstract

The overview article [1] surveyed advances related to adaptation, learning, and optimization over synchronous networks. Various distributed strategies were discussed that enable a collection of networked agents to interact locally in response to online streaming data and to continually learn and adapt to drifts in the data and models. Under reasonable technical conditions, the adaptive networks were shown to be mean-square stable in the slow adaptation regime, and their mean-square-error performance and convergence rate were characterized in terms of the network topology and data statistical properties [2]. Classical results for single-agent adaptation and learning were recovered as special cases. Following the works [3–5], this chapter complements the exposition from [1] and extends the results to asynchronous networks where agents are subject to various sources of uncertainties that influence their behavior, including randomly changing topologies, random link failures, random data arrival times, and agents turning on and off randomly. In an asynchronous environment, agents may stop updating their solutions or may stop sending or receiving information in a random manner and without coordination with other agents. The presentation will reveal that the mean-square-error performance of asynchronous networks remains largely unaltered compared to synchronous networks. The results justify the remarkable resilience of cooperative networks.