AAA: an Adaptive Mechanism for Locally Differential Private Mean Estimation
arxiv(2024)
摘要
Local differential privacy (LDP) is a strong privacy standard that has been
adopted by popular software systems. The main idea is that each individual
perturbs their own data locally, and only submits the resulting noisy version
to a data aggregator. Although much effort has been devoted to computing
various types of aggregates and building machine learning applications under
LDP, research on fundamental perturbation mechanisms has not achieved
significant improvement in recent years. Towards a more refined result utility,
existing works mainly focus on improving the worst-case guarantee. However,
this approach does not necessarily promise a better average performance given
the fact that the data in practice obey a certain distribution, which is not
known beforehand.
In this paper, we propose the advanced adaptive additive (AAA) mechanism,
which is a distribution-aware approach that addresses the average utility and
tackles the classical mean estimation problem. AAA is carried out in a two-step
approach: first, as the global data distribution is not available beforehand,
the data aggregator selects a random subset of individuals to compute a (noisy)
quantized data descriptor; then, the data aggregator collects data from the
remaining individuals, which are perturbed in a distribution-aware fashion. The
perturbation involved in the latter step is obtained by solving an optimization
problem, which is formulated with the data descriptor obtained in the former
step and the desired properties of task-determined utilities. We provide
rigorous privacy proofs, utility analyses, and extensive experiments comparing
AAA with state-of-the-art mechanisms. The evaluation results demonstrate that
the AAA mechanism consistently outperforms existing solutions with a clear
margin in terms of result utility, on a wide range of privacy constraints and
real-world and synthetic datasets.
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