Convert approx-zCDP to approx-DP with OpenDP

approx_zcdp_to_approx_dp.py

import opendp.prelude as dp


def approx_zcdp_to_approx_dp(rho: float, delta: float, delta_prime: float):
    """
    Convert a (rho, delta) approx-zCDP guarantee into an (eps, delta + delta_prime) approx-DP guarantee
    using OpenDP's measure casting and fix-delta combinators.

    Returns:
        eps (float): epsilon after conversion
        delta (float): delta + delta_prime
    """
    from opendp._internal import _make_measurement

    # given a mechanism that satisfies rho, delta...
    m_base = _make_measurement(
        input_domain=dp.atom_domain(T=bool),
        input_metric=dp.discrete_distance(),
        output_measure=dp.approximate(dp.zero_concentrated_divergence()),
        function=lambda _: (),
        privacy_map=lambda _: (rho, delta),
    )
    # convert (ρ, δ) -> (δ(ε)), δ) -> (ε, δ)
    meas_curve = dp.c.make_zCDP_to_approxDP(m_base)
    meas_fixed = dp.c.make_fix_delta(meas_curve, delta=delta + delta_prime)

    # Since the privacy map is constant, any d_in gives the same result; use d_in=1 by convention
    return meas_fixed.map(1)


dp.enable_features("contrib")
print(approx_zcdp_to_approx_dp(0.1, 5e-9, 5e-9))