Unbounded Gradients in Federated Learning with Buffered Asynchronous Aggregation

Synchronous updates may compromise the efficiency of cross-device federated learning once the number of active clients increases. The $\mathit{\text{FedBuff}}$ algorithm (Nguyen et al., 2022) alleviates this problem by allowing asynchronous updates (staleness), which enhances the scalability of training while preserving privacy via secure aggregation. We revisit the $\mathit{\text{FedBuff}}$ algorithm for asynchronous federated learning and extend the existing analysis by removing the boundedness assumptions from the gradient norm. This paper presents a theoretical analysis of the convergence rate of this algorithm when heterogeneity in data, batch size, and delay are considered.