  The possibility of adversarial (a.k.a., {\em Byzantine}) clients makes
federated learning (FL) prone to arbitrary manipulation. The natural approach
to robustify FL against adversarial clients is to replace the simple averaging
operation at the server in the standard $\mathsf{FedAvg}$ algorithm by a
\emph{robust averaging rule}. While a significant amount of work has been
devoted to studying the convergence of federated {\em robust averaging} (which
we denote by $\mathsf{FedRo}$), prior work has largely ignored the impact of
{\em client subsampling} and {\em local steps}, two fundamental FL
characteristics. While client subsampling increases the effective fraction of
Byzantine clients, local steps increase the drift between the local updates
computed by honest (i.e., non-Byzantine) clients. Consequently, a careless
deployment of $\mathsf{FedRo}$ could yield poor performance. We validate this
observation by presenting an in-depth analysis of $\mathsf{FedRo}$ tightly
analyzing the impact of client subsampling and local steps. Specifically, we
present a sufficient condition on client subsampling for nearly-optimal
convergence of $\mathsf{FedRo}$ (for smooth non-convex loss). Also, we show
that the rate of improvement in learning accuracy {\em diminishes} with respect
to the number of clients subsampled, as soon as the sample size exceeds a
threshold value. Interestingly, we also observe that under a careful choice of
step-sizes, the learning error due to Byzantine clients decreases with the
number of local steps. We validate our theory by experiments on the FEMNIST and
CIFAR-$10$ image classification tasks.
