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 clients 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.
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