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Triastcyn, Aleksei, Faltings, Boi.  2019.  Federated Learning with Bayesian Differential Privacy. 2019 IEEE International Conference on Big Data (Big Data). :2587–2596.
We consider the problem of reinforcing federated learning with formal privacy guarantees. We propose to employ Bayesian differential privacy, a relaxation of differential privacy for similarly distributed data, to provide sharper privacy loss bounds. We adapt the Bayesian privacy accounting method to the federated setting and suggest multiple improvements for more efficient privacy budgeting at different levels. Our experiments show significant advantage over the state-of-the-art differential privacy bounds for federated learning on image classification tasks, including a medical application, bringing the privacy budget below ε = 1 at the client level, and below ε = 0.1 at the instance level. Lower amounts of noise also benefit the model accuracy and reduce the number of communication rounds.
Zhao, J..  2017.  Composition Properties of Bayesian Differential Privacy. 2017 IEEE 28th Annual International Symposium on Personal, Indoor, and Mobile Radio Communications (PIMRC). :1–5.

Differential privacy is a rigorous privacy standard that has been applied to a range of data analysis tasks. To broaden the application scenarios of differential privacy when data records have dependencies, the notion of Bayesian differential privacy has been recently proposed. However, it is unknown whether Bayesian differential privacy preserves three nice properties of differential privacy: sequential composability, parallel composability, and post-processing. In this paper, we provide an affirmative answer to this question; i.e., Bayesian differential privacy still have these properties. The idea behind sequential composability is that if we have m algorithms Y1, Y2,łdots, Ym, where Y$\mathscrl$ is independently $ε\mathscrl$-Bayesian differential private for $\mathscrl$ = 1,2,łdots, m, then by feeding the result of Y1 into Y2, the result of Y2 into Y3, and so on, we will finally have an $Σ$m$\mathscrl$=;1 $ε\mathscrl$-Bayesian differential private algorithm. For parallel composability, we consider the situation where a database is partitioned into m disjoint subsets. The $\mathscrl$-th subset is input to a Bayesian differential private algorithm Y$\mathscrl$, for $\mathscrl$= 1, 2,łdots, m. Then the parallel composition of Y1, Y2,łdots, Ym will be maxm$\mathscrl$=;1=1 $ε\mathscrl$-Bayesian differential private. The postprocessing property means that a data analyst, without additional knowledge abo- t the private database, cannot compute a function of the output of a Bayesian differential private algorithm and reduce its privacy guarantee.