In recent years, Federated Learning (FL) has garnered significant attention as a distributed machine learning paradigm. To facilitate the implementation of the right to be forgotten, the concept of federated machine unlearning (FMU) has also emerged. However, current FMU approaches often involve additional time-consuming steps and may not offer comprehensive unlearning capabilities, which renders them less practical in real FL scenarios. In this paper, we introduce FedAU, an innovative and efficient FMU framework aimed at overcoming these limitations. Specifically, FedAU incorporates a lightweight auxiliary unlearning module into the learning process and employs a straightforward linear operation to facilitate unlearning. This approach eliminates the requirement for extra time-consuming steps, rendering it well-suited for FL. Furthermore, FedAU exhibits remarkable versatility. It not only enables multiple clients to carry out unlearning tasks concurrently but also supports unlearning at various levels of granularity, including individual data samples, specific classes, and even at the client level. We conducted extensive experiments on MNIST, CIFAR10, and CIFAR100 datasets to evaluate the performance of FedAU. The results demonstrate that FedAU effectively achieves the desired unlearning effect while maintaining model accuracy.

In federated learning (FL), clients usually have diverse participation probabilities that are unknown a priori, which can significantly harm the performance of FL if not handled properly. Existing works aiming at addressing this problem are usually based on global variance reduction, which requires a substantial amount of additional memory in a multiplicative factor equal to the total number of clients. An important open problem is to find a lightweight method for FL in the presence of clients with unknown participation rates. In this paper, we address this problem by adapting the aggregation weights in federated averaging (FedAvg) based on the participation history of each client. We first show that, with heterogeneous participation probabilities, FedAvg with non-optimal aggregation weights can diverge from the optimal solution of the original FL objective, indicating the need of finding optimal aggregation weights. However, it is difficult to compute the optimal weights when the participation probabilities are unknown. To address this problem, we present a new algorithm called FedAU, which improves FedAvg by adaptively weighting the client updates based on online estimates of the optimal weights without knowing the probabilities of client participation. We provide a theoretical convergence analysis of FedAU using a novel methodology to connect the estimation error and convergence. Our theoretical results reveal important and interesting insights, while showing that FedAU converges to an optimal solution of the original objective and has desirable properties such as linear speedup. Our experimental results also verify the advantage of FedAU over baseline methods.