Efficient Privacy Loss Accounting for Subsampling and Random Allocation

We consider the privacy amplification properties of a sampling scheme in which a user’s data is used in k steps chosen randomly and uniformly from a sequence (or set) of t steps. This sampling scheme has been recently applied in the context of differentially private optimization (Chua et al., 2024a; Choquette-Choo et al., 2025) and communication-efficient high-dimensional private aggregation (Asi et al., 2025), where it was shown to have utility advantages over the standard Poisson sampling. The