Federated learning enables a large number of clients to participate in learning a shared model while maintaining the training data stored in each client, which protects data privacy and security. Till now, federated learning frameworks are built in a centralized way, in which a central client is needed for collecting and distributing information from every other client. This not only leads to high communication pressure at the central client, but also renders the central client highly vulnerable to failure and attack. Here we propose a principled decentralized federated learning algorithm (DeFed), which removes the central client in the classical Federated Averaging (FedAvg) setting and only relies information transmission between clients and their local neighbors. The proposed DeFed algorithm is proven to reach the global minimum with a convergence rate of $O(1/T)$ when the loss function is smooth and strongly convex, where $T$ is the number of iterations in gradient descent. Finally, the proposed algorithm has been applied to a number of toy examples to demonstrate its effectiveness.
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