Efficient privacy loss accounting for subsampling and random allocation
Vitaly Feldman, Moshe Shenfeld
TL;DR
This work addresses the problem of tightly accounting for privacy loss under $k$-out-of-$t$ random allocation, a subsampling scheme relevant to DP-SGD and privacy-preserving communication. It develops a PLD-based framework using dominating pairs to compute the PLD of random allocation via log-sum-exp expressions and $t$-wise convolutions, with a reduction from general $k$-out-of-$t$ to the $k=1$ case. The authors provide an efficient algorithm with runtime $O(\log^{3}(t)\cdot \log(t/\beta)/\alpha^{2})$, establish discretization-based PLD realizations, and demonstrate numerically that their bounds are competitive with or tighter than prior analytic methods and Monte Carlo estimates, yielding improved privacy-utility trade-offs for DP-SGD with PREAMBLE. This PLD-centered accounting enables accurate, scalable privacy analysis for complex subsampling schemes and nested compositions, facilitating practical deployment of privacy-preserving learning and data aggregation systems.
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., 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. Theoretical analyses of this sampling scheme (Feldman & Shenfeld, 2025; Dong et al., 2025) lead to bounds that are close to those of Poisson sampling, yet still have two significant shortcomings. First, in many practical settings, the resulting privacy parameters are not tight due to the approximation steps in the analysis. Second, the computed parameters are either the hockey stick or Renyi divergence, both of which introduce overheads when used in privacy loss accounting. In this work, we demonstrate that the privacy loss distribution (PLD) of random allocation applied to any differentially private algorithm can be computed efficiently. When applied to the Gaussian mechanism, our results demonstrate that the privacy-utility trade-off for random allocation is at least as good as that of Poisson subsampling. In particular, random allocation is better suited for training via DP-SGD. To support these computations, our work develops new tools for general privacy loss accounting based on a notion of PLD realization. This notion allows us to extend accurate privacy loss accounting to subsampling which previously required manual noise-mechanism-specific analysis.