Robust Federated Primal–Dual Learning via Dynamic Graph Topology Correction under Sparse Client Participation

Federated primal–dual methods rely on client-specific dual variables to correct drift, yet sparse participation leaves most of these variables without fresh updates. Mean-based compensation addresses this missing information by assigning every inactive client the same correction, overlooking differences in their relationships with active clients. We propose RFL-DFDC, which reconstructs missing dual increments from client relationships and couples these reconstructions to the server update. A dynamic graph determines how observed increments contribute to each inactive client's virtual dual. The same weights determine the corresponding contributions to the global dual, preserving its equality to the average of virtual client duals. Our analysis bounds reconstruction error, accounts for missing graph support, and characterizes how these errors propagate to nonconvex optimization and returning clients under stated regularity conditions. Experiments on heterogeneous federated benchmarks show higher accuracy and fewer communication rounds to target accuracy than mean compensation. A comparison with a simple cosine-based alternative further supports the value of the proposed relationship weights.