  Federated Learning (FL) incurs high communication overhead, which can be
greatly alleviated by compression for model updates. Yet the tradeoff between
compression and model accuracy in the networked environment remains unclear
and, for simplicity, most implementations adopt a fixed compression rate only.
In this paper, we for the first time systematically examine this tradeoff,
identifying the influence of the compression error on the final model accuracy
with respect to the learning rate. Specifically, we factor the compression
error of each global iteration into the convergence rate analysis under both
strongly convex and non-convex loss functions. We then present an adaptation
framework to maximize the final model accuracy by strategically adjusting the
compression rate in each iteration. We have discussed the key implementation
issues of our framework in practical networks with representative compression
algorithms. Experiments over the popular MNIST and CIFAR-10 datasets confirm
that our solution effectively reduces network traffic yet maintains high model
accuracy in FL.
