Using the shuffle index, the authors formulate and solve an optimization problem for post-shuffle minimax-optimal unbiased mean estimation, yielding an asymptotically optimal mechanism whose privacy-utility tradeoff approaches the central Gaussian mechanism in the high-privacy regime.
Statistical Query Algorithms for Mean Vector Estimation and Stochastic Convex Optimization.Mathematics of Operations Research, 46(3):912–945, August 2021
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Shuffling-Aware Optimization for Private Vector Mean Estimation
Using the shuffle index, the authors formulate and solve an optimization problem for post-shuffle minimax-optimal unbiased mean estimation, yielding an asymptotically optimal mechanism whose privacy-utility tradeoff approaches the central Gaussian mechanism in the high-privacy regime.