Federated Semi-Supervised Learning with Uniform Random and Lattice-Based Client Sampling

Federated semi-supervised learning (Fed-SSL) has emerged as a powerful framework that leverages both labeled and unlabeled data distributed across clients. To reduce communication overhead, real-world deployments often adopt partial client participation, where only a subset of clients is selected in each round. However, under non-i.i.d. data distributions, the choice of client sampling strategy becomes critical, as it significantly affects training stability and final model performance. To address this challenge, we propose a novel federated averaging semi-supervised learning algorithm, called FedAvg-SSL, that considers two sampling approaches, uniform random sampling (standard Monte Carlo) and a structured lattice-based sampling, inspired by quasi-Monte Carlo (QMC) techniques, which ensures more balanced client participation through structured deterministic selection. On the client side, each selected participant alternates between updating the global model and refining the pseudo-label model using local data. We provide a rigorous convergence analysis, showing that FedAvg-SSL achieves a sublinear convergence rate with linear speedup. Extensive experiments not only validate our theoretical findings but also demonstrate the advantages of lattice-based sampling in federated learning, offering insights into the interplay among algorithm performance, client participation rates, local update steps, and sampling strategies.