Fundamental Limits of Communication Efficiency for Model Aggregation in Distributed Learning: A Rate-Distortion Approach
This addresses communication bottlenecks in distributed learning for researchers and practitioners, providing theoretical limits to guide compression methods, though it is incremental as it builds on existing rate-distortion theory.
The paper tackles the problem of unknown fundamental limits on communication cost for model aggregation in distributed learning by deriving the minimum communication rate for a given gradient distortion bound using a rate-distortion approach, finding that exploiting correlation between worker nodes yields significant gains for SignSGD and high distortion can reduce total communication cost.
One of the main focuses in distributed learning is communication efficiency, since model aggregation at each round of training can consist of millions to billions of parameters. Several model compression methods, such as gradient quantization and sparsification, have been proposed to improve the communication efficiency of model aggregation. However, the information-theoretic minimum communication cost for a given distortion of gradient estimators is still unknown. In this paper, we study the fundamental limit of communication cost of model aggregation in distributed learning from a rate-distortion perspective. By formulating the model aggregation as a vector Gaussian CEO problem, we derive the rate region bound and sum-rate-distortion function for the model aggregation problem, which reveals the minimum communication rate at a particular gradient distortion upper bound. We also analyze the communication cost at each iteration and total communication cost based on the sum-rate-distortion function with the gradient statistics of real-world datasets. It is found that the communication gain by exploiting the correlation between worker nodes is significant for SignSGD, and a high distortion of gradient estimator can achieve low total communication cost in gradient compression.