  Personalized federated learning has received an upsurge of attention due to
the mediocre performance of conventional federated learning (FL) over
heterogeneous data. Unlike conventional FL which trains a single global
consensus model, personalized FL allows different models for different clients.
However, existing personalized FL algorithms only implicitly transfer the
collaborative knowledge across the federation by embedding the knowledge into
the aggregated model or regularization. We observed that this implicit
knowledge transfer fails to maximize the potential of each client's empirical
risk toward other clients. Based on our observation, in this work, we propose
Personalized Global Federated Learning (PGFed), a novel personalized FL
framework that enables each client to personalize its own global objective by
explicitly and adaptively aggregating the empirical risks of itself and other
clients. To avoid massive (O(N^2)) communication overhead and potential privacy
leakage while achieving this, each client's risk is estimated through a
first-order approximation for other clients' adaptive risk aggregation. On top
of PGFed, we develop a momentum upgrade, dubbed PGFedMo, to more efficiently
utilize clients' empirical risks. Our extensive experiments on four datasets
under different federated settings show consistent improvements of PGFed over
previous state-of-the-art methods. The code is publicly available at
https://github.com/ljaiverson/pgfed.
