Federated learning stops trading away tail clients: keep the FedAvg direction, correct only what client constraints require

Fairness in federated aggregation can come from protecting client performance rather than rewriting the global optimization direction. Earlier fair federated methods either reweight client losses, correct conflicting gradients, or treat client losses as symmetric multi-objective common descent, and each of these changes the global update direction. On CIFAR-10, CIFAR-100 and Fashion-MNIST, across two participation rates of 5% and 10% and three heterogeneity levels, 18 configurations in total, compared with 10 fairness-aware baselines, FedPCD has the highest global accuracy in all 18 and the highest worst-10% client accuracy in 17.

The server treats the FedAvg aggregate direction as its preferred direction and departs from it only when a client progress requirement is violated. The standard FedAvg aggregate already represents the update preferred by the shared global objective, so replacing it is unnecessary when it already provides sufficient progress for the individual clients. The model displacement is divided by the local learning rate to form client pseudo-gradients, aggregated with the same weights as FedAvg into a primary direction, then a convex quadratic program seeks a direction closest to that primary direction while meeting each participating client's progress lower bound, and the solution is rescaled by the norm of the current aggregate; if the primary direction already satisfies every constraint, no directional correction is introduced.

Under partial participation, a history window lets recently unsampled clients keep influencing the update as secondary constraints. Building constraints only from clients sampled in the current round represents a narrow slice of the client population when participation is low and heterogeneity is severe. The server stores each client's most recent pseudo-gradient within a window of communication rounds as additional constraints, replaces it when the client participates again, and removes it once the window passes; an ablation shows that removing history drops CIFAR-10 global accuracy at 10% participation from 74.84 to 59.26, with worst-10% client accuracy falling as well.

The reported scope is federated training on three image classification datasets: CIFAR-10, CIFAR-100 and Fashion-MNIST, with a pool of 100 clients, participation rates of 5% and 10%, heterogeneity controlled by Dirichlet partitioning, one local epoch per client per round, and results averaged over 5 seeds. The theoretical part gives a convergence rate and a composite multi-stationarity conclusion under deterministic full participation with a fixed number of local steps. Readers following up can watch the authors' proposed adaptive progress threshold, privacy-compatible variants, and behavior under many local steps.

The progress threshold is fixed across all secondary constraints, and the authors note that the observed sensitivity to heterogeneity suggests a client- or round-dependent adaptive threshold may improve gains further. The history mechanism requires the server to observe each client's pseudo-gradient individually rather than only their aggregate, which limits applicability to secure aggregation systems. Evaluation is restricted to 100 clients and one local epoch, so behavior under many local steps, where pseudo-gradient directions degrade through client drift, is not established. The theoretical conclusions rely on full participation, deterministic local gradients and a uniform geometric alignment condition; stochastic gradients, partial participation and historical directions lie outside that theorem.