Optimal conversion from zero-concentrated to Gaussian differential privacy
Original title: Optimal Conversion from Zero-Concentrated to Gaussian Differential Privacy
Every ρ-zCDP mechanism satisfies μ_zCDP(ρ)-GDP with sharp bounds √(πρ) ≤ μ_zCDP(ρ) ≤ √(8ρ).
Paper establishes optimal reverse conversion between GDP and zCDP frameworks. Squared conversion is strictly convex, implying tighter GDP guarantee when converting before composition. Equivalence holds up to constants, explaining similar minimax risks.
- ρ-zCDP satisfies μ_zCDP(ρ)-GDP
- μ_zCDP(ρ)=2Φ^{-1}((1+e^{-t_ρ})^{-1})
- t_ρ solves ρ=t_ρ tanh(t_ρ/2)
- Squared zCDP-to-GDP conversion strictly convex
- Tighter guarantee when converting before composition
From the original article
1 min read at arxiv.orgGaussian differential privacy (GDP) and zero-concentrated differential privacy (zCDP) are two competing privacy accounting frameworks, but they share similar minimax lower bounds in various estimation problems. Moreover, it is known that a mechanism satisfying $μ$-GDP satisfies $(μ^2/2)$-zCDP, whereas the converse fails to hold at the same calibration.
By Yu-Wei Chen · arxiv.org
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