Federated Dropout is an efficient technique to overcome both communication and computation bottlenecks for deploying federated learning at the network edge. In each training round, an edge device only needs to update and transmit a sub-model, which is generated by the typical method of dropout in deep learning, and thus effectively reduces the per-round latency. \textcolor{blue}{However, the theoretical convergence analysis for Federated Dropout is still lacking in the literature, particularly regarding the quantitative influence of dropout rate on convergence}. To address this issue, by using the Taylor expansion method, we mathematically show that the gradient variance increases with a scaling factor of $\gamma/(1-\gamma)$, with $\gamma \in [0, \theta)$ denoting the dropout rate and $\theta$ being the maximum dropout rate ensuring the loss function reduction. Based on the above approximation, we provide the convergence analysis for Federated Dropout. Specifically, it is shown that a larger dropout rate of each device leads to a slower convergence rate. This provides a theoretical foundation for reducing the convergence latency by making a tradeoff between the per-round latency and the overall rounds till convergence. Moreover, a low-complexity algorithm is proposed to jointly optimize the dropout rate and the bandwidth allocation for minimizing the loss function in all rounds under a given per-round latency and limited network resources. Finally, numerical results are provided to verify the effectiveness of the proposed algorithm.

Federated learning (FL) enables distributed learning across edge devices while protecting data privacy. However, the learning accuracy decreases due to the heterogeneity of devices' data, and the computation and communication latency increase when updating large-scale learning models on devices with limited computational capability and wireless resources. We consider a FL framework with partial model pruning and personalization to overcome these challenges. This framework splits the learning model into a global part with model pruning shared with all devices to learn data representations and a personalized part to be fine-tuned for a specific device, which adapts the model size during FL to reduce both computation and communication latency and increases the learning accuracy for devices with non-independent and identically distributed data. The computation and communication latency and convergence of the proposed FL framework are mathematically analyzed. To maximize the convergence rate and guarantee learning accuracy, Karush Kuhn Tucker (KKT) conditions are deployed to jointly optimize the pruning ratio and bandwidth allocation. Finally, experimental results demonstrate that the proposed FL framework achieves a remarkable reduction of approximately 50 percent computation and communication latency compared with FL with partial model personalization.