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We study the generalization error of statistical learning models in aFederated Learning (FL) setting. Specifically, there are $K$ devices orclients, each holding an independent own dataset of size $n$. Individualmodels, learned locally via Stochastic Gradient Descent, are aggregated(averaged) by a central server into a global model and then sent back to thedevices. We consider multiple (say $R \in \mathbb N^*$) rounds of modelaggregation and study the effect of $R$ on the generalization error of thefinal aggregated model. We establish an upper bound on the generalization errorthat accounts explicitly for the effect of $R$ (in addition to the number ofparticipating devices $K$ and dataset size $n$). It is observed that, for fixed$(n, K)$, the bound increases with $R$, suggesting that the generalization ofsuch learning algorithms is negatively affected by more frequent communicationwith 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 FLalgorithms. The results of this paper, which extend straightforwardly to theheterogeneous data setting, are also illustrated through numerical examples.

More Communication Does Not Result in Smaller Generalization Error in Federated Learning