Instance-optimal Mean Estimation Under Differential Privacy
This addresses the practical utility gap in differentially private mean estimation for real-world applications, offering a principled solution that improves over heuristics.
The paper tackles the problem of mean estimation under differential privacy, where worst-case optimal mechanisms fail on real-world data with large global sensitivity, by proposing a mechanism that is instance-optimal, simple, practical, and adapts to data characteristics without tuning, extending to local and shuffle models.
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.