Federated Learning (FL) refers to the paradigm where multiple worker nodes (WNs) build a joint model by using local data. Despite extensive research, for a generic non-convex FL problem, it is not clear, how to choose the WNs' and the server's update directions, the minibatch sizes, and the local update frequency, so that the WNs use the minimum number of samples and communication rounds to achieve the desired solution. This work addresses the above question and considers a class of stochastic algorithms where the WNs perform a few local updates before communication. We show that when both the WN's and the server's directions are chosen based on certain stochastic momentum estimator, the algorithm requires $\tilde{\mathcal{O}}(\epsilon^{-3/2})$ samples and $\tilde{\mathcal{O}}(\epsilon^{-1})$ communication rounds to compute an $\epsilon$-stationary solution. To the best of our knowledge, this is the first FL algorithm that achieves such {\it near-optimal} sample and communication complexities simultaneously. Further, we show that there is a trade-off curve between local update frequencies and local minibatch sizes, on which the above sample and communication complexities can be maintained.

The aggregation efficiency and accuracy of wireless Federated Learning (FL) are significantly affected by resource constraints, especially in heterogeneous environments where devices exhibit distinct data distributions and communication capabilities. This paper proposes a clustering strategy that leverages prior knowledge similarity to group devices with similar data and communication characteristics, mitigating performance degradation from heterogeneity. On this basis, a novel Cluster- Aware Multi-round Update (CAMU) strategy is proposed, which treats clusters as the basic units and adjusts the local update frequency based on the clustered contribution threshold, effectively reducing update bias and enhancing aggregation accuracy. The theoretical convergence of the CAMU strategy is rigorously validated. Meanwhile, based on the convergence upper bound, the local update frequency and transmission power of each cluster are jointly optimized to achieve an optimal balance between computation and communication resources under constrained conditions, significantly improving the convergence efficiency of FL. Experimental results demonstrate that the proposed method effectively improves the model performance of FL in heterogeneous environments and achieves a better balance between communication cost and computational load under limited resources.

Federated Learning (FL) refers to the paradigm where multiple worker nodes (WNs) build a joint model by using local data. Despite extensive research, for a generic non-convex FL problem, it is not clear, how to choose the WNs' and the server's update directions, the minibatch sizes, and the local update frequency, so that the WNs use the minimum number of samples and communication rounds to achieve the desired solution. This work addresses the above question and considers a class of stochastic algorithms where the WNs perform a few local updates before communication. To the best of our knowledge, this is the first FL algorithm that achieves such {\it near-optimal} sample and communication complexities simultaneously. Further, we show that there is a trade-off curve between local update frequencies and local minibatch sizes, on which the above sample and communication complexities can be maintained.

Motivated by the drawbacks of cloud-based federated learning (FL), cooperative federated edge learning (CFEL) has been proposed to improve efficiency for FL over mobile edge networks, where multiple edge servers collaboratively coordinate the distributed model training across a large number of edge devices. However, CFEL faces critical challenges arising from dynamic and heterogeneous device properties, which slow down the convergence and increase resource consumption. This paper proposes a heterogeneity-aware CFEL scheme called \textit{Heterogeneity-Aware Cooperative Edge-based Federated Averaging} (HCEF) that aims to maximize the model accuracy while minimizing the training time and energy consumption via adaptive computation and communication compression in CFEL. By theoretically analyzing how local update frequency and gradient compression affect the convergence error bound in CFEL, we develop an efficient online control algorithm for HCEF to dynamically determine local update frequencies and compression ratios for heterogeneous devices. Experimental results show that compared with prior schemes, the proposed HCEF scheme can maintain higher model accuracy while reducing training latency and improving energy efficiency simultaneously.