  In this paper, we propose a novel centralized Asynchronous Federated Learning
(FL) framework, FAVANO, for training Deep Neural Networks (DNNs) in
resource-constrained environments. Despite its popularity, ``classical''
federated learning faces the increasingly difficult task of scaling synchronous
communication over large wireless networks. Moreover, clients typically have
different computing resources and therefore computing speed, which can lead to
a significant bias (in favor of ``fast'' clients) when the updates are
asynchronous. Therefore, practical deployment of FL requires to handle users
with strongly varying computing speed in communication/resource constrained
setting. We provide convergence guarantees for FAVANO in a smooth, non-convex
environment and carefully compare the obtained convergence guarantees with
existing bounds, when they are available. Experimental results show that the
FAVANO algorithm outperforms current methods on standard benchmarks.
