Instance-optimal Mean Estimation Under Differential Privacy

Part of Advances in Neural Information Processing Systems 34 pre-proceedings (NeurIPS 2021)

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Ziyue Huang, Yuting Liang, Ke Yi


Mean estimation under differential privacy is a fundamental problem, but worst-case optimal mechanisms do not offer meaningful utility guarantees in practice when the global sensitivity is very large. Instead, various heuristics have been proposed to reduce the error on real-world data that do not resemble the worst-case instance. This paper takes a principled approach, yielding a mechanism that is instance-optimal in a strong sense. In addition to its theoretical optimality, the mechanism is also simple and practical, and adapts to a variety of data characteristics without the need of parameter tuning. It easily extends to the local and shuffle model as well.