Figure 1:

An illustration of the CLT approach in the f-DP framework and the moments accountant in the (ε, δ)-DP framework. NoisyOptimizer(σ, …) using the moments accountant gives the same privacy guarantees in terms of (ε, δ)-DP as $\text{NoisyOptimizer}(\tilde{\sigma },\dots )$ using the CLT approach (the ellipses denote omitted parameters). Note that the duality formula (6) is used in solving ${\tilde{\mu }}_{\text{CLT}}$ from (7).