Federated learning (FL) is a machine learning methodology that involves the collaborative training of a global model across multiple decentralized clients in a privacy-preserving way. Several FL methods are introduced to tackle communication inefficiencies but do not address how to sample participating clients in each round effectively and in a privacy-preserving manner. In this paper, we propose \textit{FedSTaS}, a client and data-level sampling method inspired by \textit{FedSTS} and \textit{FedSampling}. In each federated learning round, \textit{FedSTaS} stratifies clients based on their compressed gradients, re-allocate the number of clients to sample using an optimal Neyman allocation, and sample local data from each participating clients using a data uniform sampling strategy. Experiments on three datasets show that \textit{FedSTaS} can achieve higher accuracy scores than those of \textit{FedSTS} within a fixed number of training rounds.

Federated learning (FL) is an important technique for learning models from decentralized data in a privacy-preserving way. Existing FL methods usually uniformly sample clients for local model learning in each round. However, different clients may have significantly different data sizes, and the clients with more data cannot have more opportunities to contribute to model training, which may lead to inferior performance. In this paper, instead of client uniform sampling, we propose a novel data uniform sampling strategy for federated learning (FedSampling), which can effectively improve the performance of federated learning especially when client data size distribution is highly imbalanced across clients. In each federated learning round, local data on each client is randomly sampled for local model learning according to a probability based on the server desired sample size and the total sample size on all available clients. Since the data size on each client is privacy-sensitive, we propose a privacy-preserving way to estimate the total sample size with a differential privacy guarantee. Experiments on four benchmark datasets show that FedSampling can effectively improve the performance of federated learning.