Analysis of Shuffling Beyond Pure Local Differential Privacy

• URL: http://arxiv.org/abs/2601.19154v1
• Date: Tue, 27 Jan 2026 03:35:03 GMT
• Title: Analysis of Shuffling Beyond Pure Local Differential Privacy
• Authors: Shun Takagi, Seng Pei Liew,
• Abstract summary: Shuffling is a powerful way to amplify privacy of a local randomizer in private distributed data analysis.<n>We develop an analysis that applies to a broad class of local randomizers under mild regularity assumptions.<n>We use an FFT-based algorithm for computing the blanket divergence at finite $n$.
• Score: 2.4264122405649045
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Shuffling is a powerful way to amplify privacy of a local randomizer in private distributed data analysis, but existing analyses mostly treat the local differential privacy (DP) parameter $\varepsilon_0$ as the only knob and give generic upper bounds that can be loose and do not even characterize how shuffling amplifies privacy for basic mechanisms such as the Gaussian mechanism. We revisit the privacy blanket bound of Balle et al. (the blanket divergence) and develop an asymptotic analysis that applies to a broad class of local randomizers under mild regularity assumptions, without requiring pure local DP. Our key finding is that the leading term of the blanket divergence depends on the local mechanism only through a single scalar parameter $χ$, which we call the shuffle index. By applying this asymptotic analysis to both upper and lower bounds, we obtain a tight band for $δ_n$ in the shuffled mechanism's $(\varepsilon_n,δ_n)$-DP guarantee. Moreover, we derive a simple structural necessary and sufficient condition on the local randomizer under which the blanket-divergence-based upper and lower bounds coincide asymptotically. $k$-RR families with $k\ge3$ satisfy this condition, while for generalized Gaussian mechanisms the condition may not hold but the resulting band remains tight. Finally, we complement the asymptotic theory with an FFT-based algorithm for computing the blanket divergence at finite $n$, which offers rigorously controlled relative error and near-linear running time in $n$, providing a practical numerical analysis for shuffle DP.

Related papers

• Unified Enhancement of Privacy Bounds for Mixture Mechanisms via $f$-Differential Privacy [41.51051636162107]
  This paper focuses on improving privacy bounds for shuffling models and one-iteration differentially private gradient descent. We derive a closed-form expression of the trade-off function for shuffling models that outperforms the most up-to-date results. We also study an $f$-DP analog of the advanced joint convexity of the hockey-stick divergence related to $(epsilon,delta)$-DP.
  arXiv  Detail & Related papers  (2023-10-30T19:37:51Z)
• Some Constructions of Private, Efficient, and Optimal $K$-Norm and Elliptic Gaussian Noise [54.34628844260993]
  Differentially private computation often begins with a bound on some $d$-dimensional statistic's sensitivity. For pure differential privacy, the $K$-norm mechanism can improve on this approach using a norm tailored to the statistic's sensitivity space. This paper solves both problems for the simple statistics of sum, count, and vote.
  arXiv  Detail & Related papers  (2023-09-27T17:09:36Z)
• General Gaussian Noise Mechanisms and Their Optimality for Unbiased Mean Estimation [58.03500081540042]
  A classical approach to private mean estimation is to compute the true mean and add unbiased, but possibly correlated, Gaussian noise to it. We show that for every input dataset, an unbiased mean estimator satisfying concentrated differential privacy introduces approximately at least as much error.
  arXiv  Detail & Related papers  (2023-01-31T18:47:42Z)
• Optimal Scaling for Locally Balanced Proposals in Discrete Spaces [65.14092237705476]
  We show that efficiency of Metropolis-Hastings (M-H) algorithms in discrete spaces can be characterized by an acceptance rate that is independent of the target distribution. Knowledge of the optimal acceptance rate allows one to automatically tune the neighborhood size of a proposal distribution in a discrete space, directly analogous to step-size control in continuous spaces.
  arXiv  Detail & Related papers  (2022-09-16T22:09:53Z)
• Gaussian Process Inference Using Mini-batch Stochastic Gradient Descent: Convergence Guarantees and Empirical Benefits [21.353189917487512]
  gradient descent (SGD) and its variants have established themselves as the go-to algorithms for machine learning problems. We take a step forward by proving minibatch SGD converges to a critical point of the full log-likelihood loss function. Our theoretical guarantees hold provided that the kernel functions exhibit exponential or eigendecay.
  arXiv  Detail & Related papers  (2021-11-19T22:28:47Z)
• Minibatch vs Local SGD with Shuffling: Tight Convergence Bounds and Beyond [63.59034509960994]
  We study shuffling-based variants: minibatch and local Random Reshuffling, which draw gradients without replacement. For smooth functions satisfying the Polyak-Lojasiewicz condition, we obtain convergence bounds which show that these shuffling-based variants converge faster than their with-replacement counterparts. We propose an algorithmic modification called synchronized shuffling that leads to convergence rates faster than our lower bounds in near-homogeneous settings.
  arXiv  Detail & Related papers  (2021-10-20T02:25:25Z)
• Optimal policy evaluation using kernel-based temporal difference methods [78.83926562536791]
  We use kernel Hilbert spaces for estimating the value function of an infinite-horizon discounted Markov reward process. We derive a non-asymptotic upper bound on the error with explicit dependence on the eigenvalues of the associated kernel operator. We prove minimax lower bounds over sub-classes of MRPs.
  arXiv  Detail & Related papers  (2021-09-24T14:48:20Z)
• Non-Euclidean Differentially Private Stochastic Convex Optimization [15.302167005107135]
  We show that noisy gradient descent (SGD) algorithms attain the optimal excess risk in low-dimensional regimes. Our work draws upon concepts from the geometry of normed spaces, such as the notions of regularity, uniform convexity, and uniform smoothness.
  arXiv  Detail & Related papers  (2021-03-01T19:48:44Z)
• Hiding Among the Clones: A Simple and Nearly Optimal Analysis of Privacy Amplification by Shuffling [49.43288037509783]
  We show that random shuffling amplifies differential privacy guarantees of locally randomized data. Our result is based on a new approach that is simpler than previous work and extends to approximate differential privacy with nearly the same guarantees.
  arXiv  Detail & Related papers  (2020-12-23T17:07:26Z)
• Tight Differential Privacy for Discrete-Valued Mechanisms and for the Subsampled Gaussian Mechanism Using FFT [6.929834518749884]
  We propose a numerical accountant for evaluating the tight $(varepsilon,delta)$-privacy loss for algorithms with discrete one dimensional output. We show that our approach allows decreasing noise variance up to 75 percent at equal privacy compared to existing bounds in the literature.
  arXiv  Detail & Related papers  (2020-06-12T12:46:42Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.