Efficient computation of the privacy loss distribution for random allocation

Vitaly Feldman, Moshe Shenfeld

Keywords: differential privacy, DP-SGD, subsampling, numerical accounting, PLD

TL;DR: We provide a direct method for tight numerical computation of the PLD for the random allocation scheme

Abstract:

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.) and communication-efficient high-dimensional private aggregation (Asi et al., 2025) as well as studied theoretically in (Feldman & Shenfeld, 2025; Dong et al.). Existing analysis techniques lead to several ways to numerically approximate the privacy parameters of random allocation yet they all suffer from two drawbacks. First, the resulting privacy parameters are not tight due the approximation steps in the analysis. Second, the computed parameters are either the hockey stick divergence or Renyi DP both of which introduce overheads when additional composition and/or subsampling are needed (such as in multi-epoch optimization algorithms).

In this work, we demonstrate that the privacy loss distribution (PLD) of random allocation applied to any differentially private algorithm can be computed efficiently. In particular, our PLD computation enables essentially lossless subsampling and composition. When applied to the Gaussian mechanism, our results demonstrate that random allocation can be used in place of Poisson subsampling with no degradation in resulting privacy guarantees.

Primary Area: alignment, fairness, safety, privacy, and societal considerations

Submission Number: 14411