  Federated learning (FL) is a decentralized and privacy-preserving machine
learning technique in which a group of clients collaborate with a server to
learn a global model without sharing clients' data. One challenge associated
with FL is statistical diversity among clients, which restricts the global
model from delivering good performance on each client's task. To address this,
we propose an algorithm for personalized FL (pFedMe) using Moreau envelopes as
clients' regularized loss functions, which help decouple personalized model
optimization from the global model learning in a bi-level problem stylized for
personalized FL. Theoretically, we show that pFedMe's convergence rate is
state-of-the-art: achieving quadratic speedup for strongly convex and sublinear
speedup of order 2/3 for smooth nonconvex objectives. Experimentally, we verify
that pFedMe excels at empirical performance compared with the vanilla FedAvg
and Per-FedAvg, a meta-learning based personalized FL algorithm.
