RDP budget curve of the Gaussian mechanism: for a query of L2
sensitivity \(\Delta\) and noise scale \(\sigma\), the mechanism
satisfies \((\alpha, \alpha \Delta^2 / (2 \sigma^2))\)-RDP for
every \(\alpha > 1\) (Mironov 2017, Proposition 7 and Corollary 3).
The curve is a straight line in \(\alpha\); n-fold composition
equals a single mechanism with scale \(\sigma / \sqrt{n}\) (remark
after Corollary 3). Conversion to (epsilon, delta)-DP is Proposition 3
and ships separately in morie_renyi_dp_composition.
Usage
Rdpc(alpha, sigma, sensitivity = 1)
Arguments
- alpha
Renyi order, must exceed 1.
- sigma
Noise standard deviation, positive.
- sensitivity
L2 sensitivity of the query, positive.
Value
List with epsilon_rdp, estimate, alpha,
sigma, sensitivity, method.
References
Mironov, I. (2017). Renyi differential privacy. IEEE CSF 2017, 263-275.
arXiv:1702.07476. Proposition 7, Corollary 3, Table II.
Examples
Rdpc(alpha = 2, sigma = 1.0)
#> $epsilon_rdp
#> [1] 1
#>
#> $estimate
#> [1] 1
#>
#> $alpha
#> [1] 2
#>
#> $sigma
#> [1] 1
#>
#> $sensitivity
#> [1] 1
#>
#> $method
#> [1] "Gaussian-mechanism RDP (Mironov 2017, Corollary 3)"
#>
#> attr(,"class")
#> [1] "morie_rich_result" "list"
