Read the equation
For each order α>1, the expression converts a valid accumulated Rényi-divergence privacy bound into an (ε,δ) bound, then selects the smallest candidate. It is the basic conversion bound associated with Mironov’s analysis. The comment’s further attribution to the current Google accountant is imprecise: Google’s inspected compute_epsilon implements a tighter conversion while retaining this basic formula in a comment, so matching a constant derived from the basic formula is not the same as reproducing that library’s current output.
Terms & definitions
| Term | Meaning in this source |
|---|---|
| alpha | Rényi order greater than one |
| rdp | Valid accumulated RDP bound |
| delta | Target failure probability between zero and one |
| epsilon | Converted privacy bound |
How it works
Read the definition from its right-hand expression to the quantity on the left. Its surrounding source records the intended input, state, or parameter context. Where the source leaves an operation unspecified, this page preserves that gap.
Assumptions & limits
The bound applies only if the actual released mechanism satisfies the input RDP accounting assumptions.
Original context
Read the surrounding source passage
} // TestPublishedGoogleRDPAccountant compares the accountant against a published Google differential privacy // RDP accountant number, QUOTED AS A FIXED CONSTANT (never by calling any external tool). // // SOURCE AND DERIVATION. For the Gaussian mechanism with noise multiplier sigma and no subsampling (q = 1), // the Renyi differential privacy at order alpha is alpha / (2 * sigma^2), and the Google dp_accounting // RdpAccountant converts accumulated RDP to (epsilon, delta) by epsilon = min over alpha of // rdp(alpha) + log(1/delta) / (alpha - 1) (Mironov 2017, Proposition 3 and Corollary 3; the same formula the // Google library uses in python/dp_accounting/rdp/rdp_privacy_accountant.py). Cited in docs/AI_RESEARCH.md, // the federated learning with differential privacy section: // // https://github.com/google/differential-privacy/tree/main/python/dp_accounting // Mironov, Renyi Differential Privacy, CSF 2017, arXiv:1702.07476. // // FIXED PUBLISHED CONSTANT. For sigma = 1.0, a single Gaussian query (no subsampling), delta = 1e-5, the // RDP accountant over a dense order grid yields the analytic optimum epsilon = 5.2985261 (optimal order // near alpha = 5.80). This is the value the Google RdpAccountant reports for the same inputs; it is reproduced
Exact original notation
RdpAccountant converts accumulated RDP to (epsilon, delta) by epsilon = min over alpha of rdp(alpha) + log(1/delta) / (alpha - 1) (Mironov 2017, Proposition 3 and Corollary 3; the same formula the