What question did this study set out to answer?

The paper aims to analyze privacy guarantees in federated learning using shuffle models, focusing on bound separation through chi-squared divergence.

January 25, 2026Open Access

Shuffle Model Privacy for Federated Learning: Asymptotic GDP Analysis and Bundled/Unbundled Separation

Key Points

The paper aims to analyze privacy guarantees in federated learning using shuffle models, focusing on bound separation through chi-squared divergence.
Employs exact asymptotic GDP parameters using chi-squared divergence.
Demonstrates exponential separation between bundled and unbundled shuffling designs.
Uses feasible SGD iterations to analyze performance.
Derives closed-form expressions for the µ-GDP parameters.
Establishes closed-form expressions for µ² under bundled and unbundled regimes.
Finds an exponential separation ratio, highlighting privacy differences.
Provides SGD iteration bounds under the µ-GDP budget.

Abstract

Exact asymptotic GDP parameters for shuffle model federated learning via chi-squared divergence. Proves exponential separation between bundled and unbundled shuffling designs in feasible SGD iterations. - After publication, the following related works were identified that share conceptual connections with this paper: 1. Su, Cheng, Wang (arXiv: 2504. 07414, 2025) analyze "joint composition" in shuffle model where user outputs are shuffled as a tuple — conceptually similar to our "bundled" regime. Their focus is on (ε, δ) -DP bounds via FFT, not µ-GDP with χ²-parameterization. 2. Su, Cheng, Wang (arXiv: 2511. 15051, 2025) show χ² (P‖Q) appears in mutual information asymptotics for shuffle model. Our contribution uses χ² for µ-GDP (differential privacy), not information-theoretic leakage. 3. Chen, Cao, Ge (AAAI 2024, arXiv: 2312. 14388) provide f-DP analysis for personalized LDP shuffle settings. They do not derive closed-form µ² expressions parameterized solely by χ² (W₁‖W₀). The core contributions of this paper remain novel: • Exact closed-form µ²₍, ₔ₍ = mχ²/n and µ²₍, ₁₃ = ( (1+χ²) ᵐ - 1) /n • Explicit exponential separation ratio Θ ( (1+χ²) ᵐ/m) • SGD iteration bounds under µ-GDP budget A revised version with expanded Related Work is planned for journal submission.

Shuffle Model Privacy for Federated Learning: Asymptotic GDP Analysis and Bundled/Unbundled Separation

Key Points

Abstract

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