Tackling Heterogeneity in Federated Learning via Variance-Reduced Boltzmann Sampling within Homogeneous Social Coalitions

Server-based federated learning (FL) enables privacy- preserving collaborative model training, but its effectiveness is often constrained by heterogeneity in client data distributions. In this paper, we address this limitation by introducing a client selection algorithm that i) dynamically forms non-overlapping coalitions of clients based on asymptotic agreement and ii) selects one representative from each coalition using a variance- reduction criterion. Our approach is inspired by social network modeling, leveraging homophily-based proximity matrices for spectral clustering and informative node selection for estimating a group’s aggregate opinion. We provide theoretical insights into the asymptotic behavior of the algorithm under explicit bounded-moment and gradient-alignment assumptions. Empirical validation against a broad set of heterogeneity-aware baselines demonstrates that our method achieves superior or highly competitive accuracy under non-IID data distributions.