Differential Private Hogwild! over Distributed Local Data Sets
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We consider the Hogwild! setting where clients use local SGD iterations with Gaussian based Differential Privacy (DP) for their own local data sets with the aim of (1) jointly converging to a global model (by interacting at a round to round basis with a centralized server that aggregates local SGD updates into a global model) while (2) keeping each local data set differentially private with respect to the outside world (this includes all other clients who can monitor client-server interactions). We show for a broad class of sample size sequences (this defines the number of local SGD iterations for each round) that a local data set is (ϵ,δ)-DP if the standard deviation σ of the added Gaussian noise per round interaction with the centralized server is at least √(2(ϵ+ ln(1/δ))/ϵ).
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