  Recently, federated learning (FL), which replaces data sharing with model
sharing, has emerged as an efficient and privacy-friendly machine learning (ML)
paradigm. One of the main challenges in FL is the huge communication cost for
model aggregation. Many compression/quantization schemes have been proposed to
reduce the communication cost for model aggregation. However, the following
question remains unanswered: What is the fundamental trade-off between the
communication cost and the FL convergence performance? In this paper, we manage
to answer this question. Specifically, we first put forth a general framework
for model aggregation performance analysis based on the rate-distortion theory.
Under the proposed analysis framework, we derive an inner bound of the
rate-distortion region of model aggregation. We then conduct an FL convergence
analysis to connect the aggregation distortion and the FL convergence
performance. We formulate an aggregation distortion minimization problem to
improve the FL convergence performance. Two algorithms are developed to solve
the above problem. Numerical results on aggregation distortion, convergence
performance, and communication cost demonstrate that the baseline model
aggregation schemes still have great potential for further improvement.
