  Federated learning (FL) is an effective solution to train machine learning
models on the increasing amount of data generated by IoT devices and
smartphones while keeping such data localized. Most previous work on federated
learning assumes that clients operate on static datasets collected before
training starts. This approach may be inefficient because 1) it ignores new
samples clients collect during training, and 2) it may require a potentially
long preparatory phase for clients to collect enough data. Moreover, learning
on static datasets may be simply impossible in scenarios with small aggregate
storage across devices. It is, therefore, necessary to design federated
algorithms able to learn from data streams. In this work, we formulate and
study the problem of \emph{federated learning for data streams}. We propose a
general FL algorithm to learn from data streams through an opportune weighted
empirical risk minimization. Our theoretical analysis provides insights to
configure such an algorithm, and we evaluate its performance on a wide range of
machine learning tasks.
