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Differential privacy is often studied under two different models ofneighboring datasets: the add-remove model and the swap model. While the swapmodel is used extensively in the academic literature, many practical librariesuse the more conservative add-remove model. However, analysis under theadd-remove model can be cumbersome, and obtaining results with tight constantsrequires some additional work. Here, we study the problem of one-dimensionalmean estimation under the add-remove model of differential privacy. We proposea new algorithm and show that it is min-max optimal, that it has the correctconstant in the leading term of the mean squared error, and that this constantis the same as the optimal algorithm in the swap model. Our results show that,for mean estimation, the add-remove and swap model give nearly identical erroreven though the add-remove model cannot treat the size of the dataset as publicinformation. In addition, we demonstrate empirically that our proposedalgorithm yields a factor of two improvement in mean squared error overalgorithms often used in practice.

Mean estimation in the add-remove model of differential privacy