  Federated learning (FL) is a training paradigm where the clients
collaboratively learn models by repeatedly sharing information without
compromising much on the privacy of their local sensitive data. In this paper,
we introduce federated $f$-differential privacy, a new notion specifically
tailored to the federated setting, based on the framework of Gaussian
differential privacy. Federated $f$-differential privacy operates on record
level: it provides the privacy guarantee on each individual record of one
client's data against adversaries. We then propose a generic private federated
learning framework {PriFedSync} that accommodates a large family of
state-of-the-art FL algorithms, which provably achieves federated
$f$-differential privacy. Finally, we empirically demonstrate the trade-off
between privacy guarantee and prediction performance for models trained by
{PriFedSync} in computer vision tasks.
