The privacy concern exists when the central server has the copies of datasets. Hence, there is a paradigm shift for the learning networks to change from centralized in-cloud learning to distributed \mbox{on-device} learning. Benefit from the parallel computing, the on-device learning networks have a lower bandwidth requirement than the in-cloud learning networks. Moreover, the on-device learning networks also have several desirable characteristics such as privacy preserving and flexibility. However, the \mbox{on-device} learning networks are vulnerable to the malfunctioning terminals across the networks. The worst-case malfunctioning terminals are the Byzantine adversaries, that can perform arbitrary harmful operations to compromise the learned model based on the full knowledge of the networks. Hence, the design of secure learning algorithms becomes an emerging topic in the on-device learning networks with Byzantine adversaries. In this article, we present a comprehensive overview of the prevalent secure learning algorithms for the two promising on-device learning networks: Federated-Learning networks and decentralized-learning networks. We also review several future research directions in the \mbox{Federated-Learning} and decentralized-learning networks.
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