Cycwin-FL: Convergence for Federated Learning with Cyclic-Window Client Availability

In resource-constrained federated learning (FL), client availability may be restricted by computing power, connectivity or privacy requirements, thus entailing *controlled* client participation. This prohibits direct application of existing convergence-analysis frameworks under the simplified assumption of full or uniform client sampling. Recent studies on convergence for FL with cyclic client participation schemes often considered restricted types of training objectives or specific cyclic patterns. In this paper, we investigate FL with a *general deterministic cyclic pattern*, i.e., *Cycwin-FL*, which applies FedAvg with uniform client sampling from within a window of $B$ among $M$ clients that cyclically advances by $N_w$ clients per communication round. We provide convergence analysis for Cycwin-FL with Polyak-Łojasiewicz (PL)-conditioned and general smooth non-convex objectives, respectively. Specifically, if $\gcd (M,N_w)\mid B$ is satisfied, for PL-conditioned objectives, we reveal an $\tilde{\mathcal{O}}(T^{-1})$ upper bound on the optimality gap leveraging window-induced bias cancellation, where $T$ is the total number of communication rounds; and for general smooth non-convex objectives, we derive the same $\mathcal{O}(T^{-1/2})$ convergence rate as the vanilla FedAvg. In addition, we also quantify the impact of failure in meeting the condition $\gcd (M,N_w)\mid B$ on convergence. Finally, experiments validate our theoretical insights into the effect of the cyclic patterns.