Zero-concentrated DP composition

rho adds exactly across mechanisms, and converts as \(\epsilon = \rho + 2\sqrt{\rho\log(1/\delta)}\).

Usage

morie_cdp_subgaussian_amplification(rho, k_compositions = 1, delta = 1e-05)

Arguments

rho

per-mechanism rho values, or a single rho.

k_compositions

repetitions when rho is scalar.

delta

target delta for the conversion.

Value

list with rho_total, epsilon, equivalent_sigma.

Details

The \(\sqrt k\) growth that advanced composition has to buy with a union bound comes FREE here, because rho is additive and the square root appears only once in the conversion. That is the reason to account in zCDP.

What zCDP cannot do is represent pure epsilon-DP: the Laplace mechanism has unbounded Renyi divergence at large orders and no finite rho exists for it.

References

Bun, M. and Steinke, T. (2016). Concentrated differential privacy: simplifications, extensions, and lower bounds. TCC, 635-658.

Examples

round(morie_cdp_subgaussian_amplification(0.01, 100)$epsilon, 4)
#> [1] 7.7861