Over the past few years, Federated Learning (FL) has become a popular distributed machine learning paradigm. FL involves a group of clients with decentralized data who collaborate to learn a common model under the coordination of a centralized server, with the goal of protecting clients' privacy by ensuring that local datasets never leave the clients and that the server only performs model aggregation. However, in realistic scenarios, the server may be able to collect a small amount of data that approximately mimics the population distribution and has stronger computational ability to perform the learning process. To address this, we focus on the hybrid FL framework in this paper. While previous hybrid FL work has shown that the alternative training of clients and server can increase convergence speed, it has focused on the scenario where clients fully participate and ignores the negative effect of partial participation. In this paper, we provide theoretical analysis of hybrid FL under clients' partial participation to validate that partial participation is the key constraint on convergence speed. We then propose a new algorithm called FedCLG, which investigates the two-fold role of the server in hybrid FL. Firstly, the server needs to process the training steps using its small amount of local datasets. Secondly, the server's calculated gradient needs to guide the participated clients' training and the server's aggregation. We validate our theoretical findings through numerical experiments, which show that our proposed method FedCLG outperforms state-of-the-art methods.
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