  Asynchronous Federated Learning with Buffered Aggregation (FedBuff) is a
state-of-the-art algorithm known for its efficiency and high scalability.
However, it has a high communication cost, which has not been examined with
quantized communications. To tackle this problem, we present a new algorithm
(QAFeL), with a quantization scheme that establishes a shared "hidden" state
between the server and clients to avoid the error propagation caused by direct
quantization. This approach allows for high precision while significantly
reducing the data transmitted during client-server interactions. We provide
theoretical convergence guarantees for QAFeL and corroborate our analysis with
experiments on a standard benchmark.
