Lower Bounds and Optimal Algorithms for Personalized Federated Learning
This provides provably optimal algorithms for personalized federated learning, addressing efficiency in distributed machine learning.
The authors established the first lower bounds for communication and local oracle complexity in personalized federated learning, and designed optimal methods matching these bounds, including accelerated variants of FedProx and FedAvg/Local SGD.
In this work, we consider the optimization formulation of personalized federated learning recently introduced by Hanzely and Richtárik (2020) which was shown to give an alternative explanation to the workings of local {\tt SGD} methods. Our first contribution is establishing the first lower bounds for this formulation, for both the communication complexity and the local oracle complexity. Our second contribution is the design of several optimal methods matching these lower bounds in almost all regimes. These are the first provably optimal methods for personalized federated learning. Our optimal methods include an accelerated variant of {\tt FedProx}, and an accelerated variance-reduced version of {\tt FedAvg}/Local {\tt SGD}. We demonstrate the practical superiority of our methods through extensive numerical experiments.