Convergence under state-dependent device selection

Establish end-to-end convergence guarantees for NCAirFL when the device-selection policy is state-dependent and selects devices using statistics such as the estimated first- and second-order innovation moments and power constraints, rather than uniform random participation.

Background

The convergence result for NCAirFL in Proposition 1 is established under uniform sampling without replacement, which makes the active-device average an unbiased estimator of the global-average update. In contrast, Algorithm 2 deterministically selects devices according to state-dependent statistics, including the estimated norms of the preprocessed innovations, together with power constraints. Such selection favors devices with larger estimated gradient-descent contributions and more favorable channel conditions, so the unbiasedness argument used for uniform participation no longer directly applies.

The paper notes that related non-uniform scheduling methods optimize a lower bound on one-round loss reduction without addressing global convergence, whereas probability-aware scheduling can preserve unbiased aggregation. A remaining problem is therefore to extend the convergence analysis of NCAirFL to the deterministic, state-dependent device-selection policy used by the proposed optimization framework.