Brief paper - Asynchronous algorithms for distributed optimisation and application to distributed regression with robustness to outliers

This study presents an asynchronous algorithm for distributed constrained optimisation problems in networks of agents. The iterative optimisation algorithm maintains a local estimate at each node and depends on local gradient or gradient-like updates in combination with a consensus policy, where an agent averages its own value with a current or outdated value of another. This asynchronous scheme does not require that agents exchange state information frequently, so it is more energy-efficient and more realistic than the synchronous one. Moreover, the proposed algorithm is fully distributed, that is, all agents only share data with their neighbours through local broadcasts. The proposed algorithm is applied to a distributed regression problem with robustness to outliers in sensor networks. Simulation results are provided to demonstrate the validity and superiority of the proposed scheme.