Partial Participation: Guarantees of Local Step Convergence for Unified Client Selection in the Non-Convex Case

Federated learning enables model training across distributed devices without direct data sharing, making it a natural framework for large-scale learning systems. Its scalability is nevertheless constrained by two fundamental bottlenecks: server-side overload caused by the impossibility of involving all devices in each communication round, and channel overload caused by transmitting high-dimensional models. These challenges are traditionally addressed separately: the former through partial participation training paradigm, and the latter through compression of the transmitted information. In heterogeneous settings, however, standard partial participation schemes may lead to biased optimization dynamics and are difficult to analyze rigorously. While partial participation and compression have been extensively studied in isolation, their joint treatment under heterogeneity remains largely unresolved. In this work, we address this gap by developing a novel federated optimization algorithm that operates under partial participation with compressed communication. We establish convergence guarantees under general non-convex assumptions and empirically evaluate the proposed method on image classification benchmarks.