High-Probability Bounds for Heterogeneous Local Differential Privacy

Maryam Aliakbarpour, Alireza Fallah, Swaha Roy, Ria Stevens
Proceedings of The 29th International Conference on Artificial Intelligence and Statistics, PMLR 300:3709-3717, 2026.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v300-aliakbarpour26b, title = { High-Probability Bounds for Heterogeneous Local Differential Privacy }, author = {Aliakbarpour, Maryam and Fallah, Alireza and Roy, Swaha and Stevens, Ria}, booktitle = {Proceedings of The 29th International Conference on Artificial Intelligence and Statistics}, pages = {3709--3717}, year = {2026}, editor = {Khan, Emtiyaz and Li, Yingzhen and Solin, Arno and Ramdas, Aaditya}, volume = {300}, series = {Proceedings of Machine Learning Research}, month = {02--05 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v300/main/assets/aliakbarpour26b/aliakbarpour26b.pdf}, url = {https://proceedings.mlr.press/v300/aliakbarpour26b.html}, 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. } }
Endnote
%0 Conference Paper %T High-Probability Bounds for Heterogeneous Local Differential Privacy %A Maryam Aliakbarpour %A Alireza Fallah %A Swaha Roy %A Ria Stevens %B Proceedings of The 29th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2026 %E Emtiyaz Khan %E Yingzhen Li %E Arno Solin %E Aaditya Ramdas %F pmlr-v300-aliakbarpour26b %I PMLR %P 3709--3717 %U https://proceedings.mlr.press/v300/aliakbarpour26b.html %V 300 %X 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.
APA
Aliakbarpour, M., Fallah, A., Roy, S. & Stevens, R.. (2026). High-Probability Bounds for Heterogeneous Local Differential Privacy . Proceedings of The 29th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 300:3709-3717 Available from https://proceedings.mlr.press/v300/aliakbarpour26b.html.

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