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    Abstract We explore the power of the hybrid model of differential privacy (DP), in which some users desire the guarantees of the local model of DP and others are content with receiving the trusted-curator model guarantees. In particular, we study the utility of hybrid model estimators that compute the mean of arbitrary realvalued distributions with bounded support. When the curator knows the distribution’s variance, we design a hybrid estimator that, for realistic datasets and parameter settings, achieves a constant factor improvement over natural baselines.We then analytically characterize how the estimator’s utility is parameterized by the problem setting and parameter choices. When the distribution’s variance is unknown, we design a heuristic hybrid estimator and analyze how it compares to the baselines. We find that it often performs better than the baselines, and sometimes almost as well as the known-variance estimator. We then answer the question of how our estimator’s utility is affected when users’ data are not drawn from the same distribution, but rather from distributions dependent on their trust model preference. Concretely, we examine the implications of the two groups’ distributions diverging and show that in some cases, our estimators maintain fairly high utility. We then demonstrate how our hybrid estimator can be incorporated as a sub-component in more complex, higher-dimensional applications. Finally, we propose a new privacy amplification notion for the hybrid model that emerges due to interaction between the groups, and derive corresponding amplification results for our hybrid estimators. 
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  5. Tauman Kalai, Yael ; Smith, Adam D ; Wichs, Daniel (Ed.)
    Motivated by the desire to bridge the utility gap between local and trusted curator models of differential privacy for practical applications, we initiate the theoretical study of a hybrid model introduced by "Blender" [Avent et al., USENIX Security '17], in which differentially private protocols of n agents that work in the local-model are assisted by a differentially private curator that has access to the data of m additional users. We focus on the regime where m ≪ n and study the new capabilities of this (m,n)-hybrid model. We show that, despite the fact that the hybrid model adds no significant new capabilities for the basic task of simple hypothesis-testing, there are many other tasks (under a wide range of parameters) that can be solved in the hybrid model yet cannot be solved either by the curator or by the local-users separately. Moreover, we exhibit additional tasks where at least one round of interaction between the curator and the local-users is necessary - namely, no hybrid model protocol without such interaction can solve these tasks. Taken together, our results show that the combination of the local model with a small curator can become part of a promising toolkit for designing and implementing differential privacy. 
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  6. We propose a hybrid model of differential privacy that considers a combination of regular and opt-in users who desire the differential privacy guarantees of the local privacy model and the trusted curator model, respectively. We demonstrate that within this model, it is possible to design a new type of blended algorithm that improves the utility of obtained data, while providing users with their desired privacy guarantees. We apply this algorithm to the task of privately computing the head of the search log and show that the blended approach provides significant improvements in the utility of the data compared to related work. Specifically, on two large search click data sets, comprising 1.75 and 16 GB, respectively, our approach attains NDCG values exceeding 95% across a range of privacy budget values. 
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