  Distributed Mean Estimation (DME) is a central building block in federated
learning, where clients send local gradients to a parameter server for
averaging and updating the model. Due to communication constraints, clients
often use lossy compression techniques to compress the gradients, resulting in
estimation inaccuracies.
  DME is more challenging when clients have diverse network conditions, such as
constrained communication budgets and packet losses. In such settings, DME
techniques often incur a significant increase in the estimation error leading
to degraded learning performance.
  In this work, we propose a robust DME technique named EDEN that naturally
handles heterogeneous communication budgets and packet losses. We derive
appealing theoretical guarantees for EDEN and evaluate it empirically. Our
results demonstrate that EDEN consistently improves over state-of-the-art DME
techniques.
