  Synchronous updates may compromise the efficiency of cross-device federated
learning once the number of active clients increases. The \textit{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
\textit{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.
