  We study the generalization error of statistical learning models in a
Federated Learning (FL) setting. Specifically, there are $K$ devices or
clients, each holding an independent own dataset of size $n$. Individual
models, learned locally via Stochastic Gradient Descent, are aggregated
(averaged) by a central server into a global model and then sent back to the
devices. We consider multiple (say $R \in \mathbb N^*$) rounds of model
aggregation and study the effect of $R$ on the generalization error of the
final aggregated model. We establish an upper bound on the generalization error
that accounts explicitly for the effect of $R$ (in addition to the number of
participating devices $K$ and dataset size $n$). It is observed that, for fixed
$(n, K)$, the bound increases with $R$, suggesting that the generalization of
such learning algorithms is negatively affected by more frequent communication
with the parameter server. Combined with the fact that the empirical risk,
however, generally decreases for larger values of $R$, this indicates that $R$
might be a parameter to optimize to reduce the population risk of FL
algorithms. The results of this paper, which extend straightforwardly to the
heterogeneous data setting, are also illustrated through numerical examples.
