Rate Region for Indirect Multiterminal Source Coding in Federated Learning

One of the main focus in federated learning (FL) is the communication efficiency since a large number of participating edge devices send their updates to the edge server at each round of the model training. Existing works reconstruct each model update from edge devices and implicitly assume that the local model updates are independent over edge device. In FL, however, the model update is an indirect multi-terminal source coding problem where each edge device cannot observe directly the source that is to be reconstructed at the decoder, but is rather provided only with a noisy version. The existing works do not leverage the redundancy in the information transmitted by different edges. This paper studies the rate region for the indirect multiterminal source coding problem in FL. The goal is to obtain the minimum achievable rate at a particular upper bound of gradient variance. We obtain the rate region for multiple edge devices in general case and derive an explicit formula of the sum-rate distortion function in the special case where gradient are identical over edge device and dimension. Finally, we analysis communication efficiency of convex Mini-batched SGD and non-convex Minibatched SGD based on the sum-rate distortion function, respectively.