High-Probability Bounds For Heterogeneous Local Differential Privacy

• URL: http://arxiv.org/abs/2510.11895v1
• Date: Mon, 13 Oct 2025 19:54:44 GMT
• Title: High-Probability Bounds For Heterogeneous Local Differential Privacy
• Authors: Maryam Aliakbarpour, Alireza Fallah, Swaha Roy, Ria Stevens,
• Abstract summary: We study statistical estimation under local differential privacy (LDP)<n>We develop finite sample upper bounds in $ell$-norm that hold probability with at least $1-beta.<n>We further study distribution learning in $ell_infty$-distance, designing an algorithm with high-probability guarantees under heterogeneous privacy demands.
• Score: 6.092107731520248
• License: http://creativecommons.org/licenses/by/4.0/
• 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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