Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Optimal Noise-Adding Mechanism in Additive Differential Privacy   We derive the optimal $(0, \delta)$-differentially private query-output
independent noise-adding mechanism for single real-valued query function under
a general cost-minimization framework. Under a mild technical condition, we
show that the optimal noise probability distribution is a uniform distribution
with a probability mass at the origin. We explicitly derive the optimal noise
distribution for general $\ell^p$ cost functions, including $\ell^1$ (for noise
magnitude) and $\ell^2$ (for noise power) cost functions, and show that the
probability concentration on the origin occurs when $\delta > \frac{p}{p+1}$.
Our result demonstrates an improvement over the existing Gaussian mechanisms by
a factor of two and three for $(0,\delta)$-differential privacy in the high
privacy regime in the context of minimizing the noise magnitude and noise
power, and the gain is more pronounced in the low privacy regime. Our result is
consistent with the existing result for $(0,\delta)$-differential privacy in
the discrete setting, and identifies a probability concentration phenomenon in
the continuous setting.

10
The categories of this paper are: q-bio
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat
33
The categories of this paper are: plasm-ph
15
The categories of this paper are: nucl-ex
7
The categories of this paper are: hep-th
24
The categories of this paper are: dg-ga
18
The categories of this paper are: econ
32
The categories of this paper are: atom-ph
2
The categories of this paper are: math
13
The categories of this paper are: quant-ph
29
The categories of this paper are: funct-an