  Traditional federated learning algorithms impose strict requirements on the
participation rates of devices, which limit the potential reach of federated
learning. This paper extends the current learning paradigm to include devices
that may become inactive, compute incomplete updates, and depart or arrive in
the middle of training. We derive analytical results to illustrate how allowing
more flexible device participation can affect the learning convergence when
data is not independently and identically distributed (non-IID). We then
propose a new federated aggregation scheme that converges even when devices may
be inactive or return incomplete updates. We also study how the learning
process can adapt to early departures or late arrivals, and analyze their
impacts on the convergence.
