RDP epsilons at a fixed order alpha compose EXACTLY additively –
that is the whole reason to account in RDP rather than in
(epsilon, delta). Conversion back costs
\(\log(1/\delta)/(\alpha-1)\).
Usage
morie_renyi_dp_composition(epsilons, alpha = 2, delta = 1e-05)
Arguments
- epsilons
vector of per-mechanism RDP epsilons at order alpha.
- alpha
Renyi order, greater than 1.
- delta
target delta for the conversion.
Value
list with rdp_total, epsilon (converted),
conversion_penalty.
Details
Because the conversion penalty falls with alpha while the RDP total
rises with it, the final epsilon is minimised at some interior alpha.
Account first, then sweep alpha; picking alpha up front leaves budget
on the table.
References
Mironov, I. (2017). Renyi differential privacy.
CSF, 263-275.
Examples
round(morie_renyi_dp_composition(rep(0.1, 10), alpha = 4)$epsilon, 4)
#> [1] 4.8376
