提出新方法提升私有向量均值估计精度，突破传统隐私保护限制。
Shuffling-Aware Optimization for Private Vector Mean Estimation
- 基于洗牌索引构建优化框架，精准刻画洗牌后隐私机制性能
- 证明最优本地隐私机制在洗牌下可能失效，需重新设计
- 构造高隐私场景下近最优机制，媲美中心化高斯机制
研究在单消息洗牌模型下的 d 维无偏均值估计问题，其中每位用户发送一条隐私化消息，分析者仅观察到报告的随机洗牌多重集。尽管本地差分隐私（LDP）下的极小极大最优机制已有深入理解，但洗牌后的最优性概念仍不明确。为此，本文引入近期提出的洗牌索引，将洗牌后机制设计转化为显式优化问题。我们建立了均方误差的极小极大下界，其与洗牌索引相关，表明在洗牌后，原本在 LDP 下最优的机制可能变得次优。最后，我们构造了一个高隐私区域下的渐近极小极大最优机制，其隐私-效用权衡几乎等同于中心化高斯机制。
原文摘要 · Abstract (English)
We study $d$-dimensional unbiased mean estimation in the single-message shuffle model, where each user sends a single privatized message and the analyzer only observes the shuffled multiset of reports. While minimax-optimal mechanisms are well understood in the local differential privacy setting, the corresponding notion of optimality after shuffling has remained largely unexplored. To address this gap, we introduce the recently proposed shuffle index and use it to formulate the post-shuffling mechanism design problem as an explicit optimization problem. We then establish a minimax lower bound on the achievable mean squared error in terms of the shuffle index, which implies that mechanisms that are optimal under LDP can become suboptimal once shuffling is applied. Finally, we construct an asymptotically minimax optimal mechanism in the high privacy regime, which as a consequence achieves a privacy-utility trade-off nearly identical to that of the central Gaussian mechanism.
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