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.
Analysis of Shuffling Beyond Pure Local Differential Privacy, January
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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.