Evolution of the separation metric under multi-epoch composition

Characterize how the separation metric κ = sep(f) of the f-differential privacy trade-off curve evolves under repeated composition across multiple epochs of differentially private stochastic gradient descent (DP-SGD) in the worst-case adversarial model, and extend the single-epoch separation lower bounds to the multi-epoch regime by deriving explicit, non-asymptotic guarantees.

Background

The paper introduces a geometric separation metric κ that measures the maximum Euclidean distance between the f-DP trade-off curve and the ideal random-guessing line. It proves single-epoch lower bounds on κ for shuffled DP-SGD (and, up to constants, for Poisson subsampling), showing a fundamental privacy–utility tension when noise levels are below a threshold.

While practice typically involves many epochs, existing μ-GDP analyses provide only asymptotic convergence results and do not directly characterize κ or supply non-asymptotic rates under composition. The authors therefore highlight the need to understand how κ behaves when DP-SGD updates are composed over multiple epochs and to extend their single-epoch bounds to this practical multi-epoch setting.