Lower bound on additive error when releasing vector of values differentially privately

user167622

8/27/24, 3:34 PM

I have a vector of $n$ elements where each entry is a non-negative integer. Neighboring vectors differ in one element where the absolute value difference between the elements that differ is $1$. I want to release the entire vector differentially privately. We can do this easily using the Laplace mechanism with sensitivity $1$, which results in the expected maximum noise added to any value to be $\Theta((\log n)/\epsilon)$. However, I would like to know whether there are any lower bounds on the expected maximum additive error of any release element. Are there any previous works showing similar lower bounds to this problem?

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algorithm-design

differential-privacy

Elon Musk

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EN: Lower bound on additive error when releasing vector of values differentially privately

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