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This relation defines RDP accountant over a dense order grid yields the analytic optimum epsilon in the source section “func TestCompositionMonotonicity(t *testing.T) · RDP accountant over a dense order grid yields the analytic optimum epsilon”. It specifies the displayed relationship between the named quantities or parameters. Its interpretation depends on the source’s stated variables and conditions; this record does not assign an unprovided physical or cognitive meaning to them.
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Original context
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// 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
// here ONLY as a quoted constant, not by calling the library. The accountant's shipped coarse grid lands at
// 5.3025851 (optimal order 6 on the grid), which is a SOUND UPPER BOUND: the min over a coarser grid is never
// below the dense optimum, so the accountant can only overstate epsilon, never understate it (the safe
// direction for a privacy claim).
func TestPublishedGoogleRDPAccountant(t *testing.T) {
const publishedDenseOptimum = 5.2985261 // sigma=1, single query, delta=1e-5, dense grid analytic optimum
// Reproduce the dense grid optimum here (a denser order set than the shipped grid) and check it matches
// the published constant. This proves the conversion formula itself is the published one.Exact original notation
RDP accountant over a dense order grid yields the analytic optimum epsilon = 5.2985261 (optimal order