  Federated learning (FL) is becoming a major driving force behind machine
learning as a service, where customers (clients) collaboratively benefit from
shared local updates under the orchestration of the service provider (server).
Representing clients' current demands and the server's future demand, local
model personalization and global model generalization are separately
investigated, as the ill-effects of data heterogeneity enforce the community to
focus on one over the other. However, these two seemingly competing goals are
of equal importance rather than black and white issues, and should be achieved
simultaneously. In this paper, we propose the first algorithm to balance
personalization and generalization on top of game theory, dubbed PAGE, which
reshapes FL as a co-opetition game between clients and the server. To explore
the equilibrium, PAGE further formulates the game as Markov decision processes,
and leverages the reinforcement learning algorithm, which simplifies the
solving complexity. Extensive experiments on four widespread datasets show that
PAGE outperforms state-of-the-art FL baselines in terms of global and local
prediction accuracy simultaneously, and the accuracy can be improved by up to
35.20% and 39.91%, respectively. In addition, biased variants of PAGE imply
promising adaptiveness to demand shifts in practice.
