High-Probability Bounds for Heterogeneous Local Differential Privacy

Maryam Aliakbarpour, Alireza Fallah, Swaha Roy, Ria Stevens

Abstract: We study statistical estimation under local differential privacy (LDP) when users may hold heterogeneous privacy levels and accuracy must be guaranteed with high probability. Departing from the common in-expectation analyses, and for one-dimensional and multi-dimensional mean estimation problems, we develop finite sample upper bounds in $\ell_2$-norm that hold with probability at least $1-\beta$. We complement these results with matching minimax lower bounds, establishing the optimality (up to constants) of our guarantees in the heterogeneous LDP regime. We further study distribution learning in $\ell_\infty$-distance, designing an algorithm with high-probability guarantees under heterogeneous privacy demands. Our techniques offer principled guidance for designing mechanisms in settings with user-specific privacy levels.

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Code Dataset Url: https://github.com/swaharoy/Mean-Estimation-under-Heterogeneous-LDP

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Submission Number: 1587