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Convergent Differential Privacy Analysis for General Federated Learning

ICLR 2026 Conference SubmissionAnonymous Authors
OpenReview Score: 6.0Download Report PDF
Differential privacyfederated learning
Abstract:

The powerful cooperation of federated learning (FL) and differential privacy (DP) provides a promising paradigm for the large-scale private clients. However, existing analyses in FL-DP mostly rely on the composition theorem and cannot tightly quantify the privacy leakage challenges, which is tight for a few communication rounds but yields an arbitrarily loose and divergent bound eventually. This also implies a counterintuitive judgment, suggesting that FL-DP may not provide adequate privacy support during long-term training under constant-level noisy perturbations, yielding discrepancy between the theoretical and experimental results. To further investigate the convergent privacy and reliability of the FL-DP framework, in this paper, we comprehensively evaluate the worst privacy of two classical methods under the non-convex and smooth objectives based on the ff-DP analysis. With the aid of the shifted interpolation technique, we successfully prove that privacy in Noisy-FedAvg has a tight convergent bound. Moreover, with the regularization of the proxy term, privacy in Noisy-FedProx has a stable constant lower bound. Our analysis further demonstrates a solid theoretical foundation for the reliability of privacy in FL-DP. Meanwhile, our conclusions can also be losslessly converted to other classical DP analytical frameworks, e.g. (ϵ,δ)(\epsilon,\delta)-DP and Reˊ\'{e}nyi-DP (RDP), to provide more fine-grained understandings for the FL-DP frameworks.

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This report is AI-GENERATED using Large Language Models and WisPaper (A scholar search engine). It analyzes academic papers' tasks and contributions against retrieved prior work. While this system identifies POTENTIAL overlaps and novel directions, ITS COVERAGE IS NOT EXHAUSTIVE AND JUDGMENTS ARE APPROXIMATE. These results are intended to assist human reviewers and SHOULD NOT be relied upon as a definitive verdict on novelty.
NOTE that some papers exist in multiple, slightly different versions (e.g., with different titles or URLs). The system may retrieve several versions of the same underlying work. The current automated pipeline does not reliably align or distinguish these cases, so human reviewers will need to disambiguate them manually.
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Overview

Overall Novelty Assessment

This paper develops convergent privacy bounds for Noisy-FedAvg and Noisy-FedProx under non-convex objectives using f-DP analysis and shifted interpolation techniques. It resides in the 'Convergence and Privacy Trade-off Analysis' leaf, which contains five papers total including the original work. This leaf sits within the broader 'Privacy Analysis Frameworks and Theoretical Foundations' branch, indicating a moderately populated research direction focused on formal privacy guarantees rather than algorithm design or system implementation. The sibling papers in this leaf similarly examine convergence-privacy trade-offs, suggesting this is an active but not overcrowded theoretical niche.

The taxonomy reveals neighboring leaves addressing 'Privacy Amplification and Accounting Mechanisms' (four papers) and 'Clipping and Noise Injection Analysis' (three papers), both within the same theoretical foundations branch. These adjacent directions explore complementary aspects: amplification techniques and moments accountant methods versus gradient clipping strategies. The paper's use of f-DP and shifted interpolation connects it to the amplification leaf's advanced accounting methods, while its focus on Noisy-FedAvg and Noisy-FedProx links it to the clipping leaf's noise perturbation strategies. The taxonomy's scope and exclude notes clarify that this work belongs in theoretical analysis rather than pure algorithm design, distinguishing it from the 'Federated Learning Algorithm Design with Differential Privacy' branch.

Among twenty-three candidates examined across three contributions, none were identified as clearly refuting the paper's claims. The first contribution (convergent privacy for Noisy-FedAvg) examined nine candidates with zero refutable matches; the second (Noisy-FedProx with constant lower bound) examined ten candidates with zero refutable matches; the third (f-DP framework with shifted interpolation) examined four candidates with zero refutable matches. This suggests that within the limited search scope, the specific combination of f-DP analysis, shifted interpolation, and convergent bounds for these two algorithms appears relatively unexplored. However, the search examined only top-K semantic matches and citations, not the entire literature.

Based on the limited analysis of twenty-three candidates, the work appears to occupy a distinct position within convergence-privacy trade-off research. The absence of refutable prior work among examined candidates suggests novelty in the specific technical approach, though the search scope does not cover all possible related work in privacy accounting or federated optimization. The taxonomy context indicates this contribution extends an active theoretical research direction rather than opening an entirely new area.

Taxonomy

Core-task Taxonomy Papers
50
3
Claimed Contributions
23
Contribution Candidate Papers Compared
0
Refutable Paper

Research Landscape Overview

Core task: convergent differential privacy analysis for federated learning. The field organizes around several major branches that reflect distinct emphases in privacy-preserving distributed machine learning. Privacy Analysis Frameworks and Theoretical Foundations focuses on rigorous convergence and privacy trade-off analysis, examining how noise injection affects learning guarantees under various privacy models such as local, central, and shuffled differential privacy. Federated Learning Algorithm Design with Differential Privacy and Distributed Optimization with Differential Privacy develop concrete algorithmic strategies—ranging from gradient perturbation methods like DP-SGD to ADMM-based approaches—that balance model accuracy with formal privacy budgets. Communication and Computation Efficiency Enhancements and Communication-Efficient Privacy-Preserving Distributed Learning address the practical overhead of adding noise and transmitting updates, exploring quantization, sparsification, and adaptive local steps to reduce bandwidth costs. Meanwhile, Privacy-Preserving Collaborative Learning Systems and Trustworthy and Scalable Collaborative Learning Frameworks tackle system-level concerns including asynchronous aggregation, Byzantine robustness, and verifiable computation, while Application-Specific Privacy-Preserving Learning and Privacy-Utility Trade-offs and Incentive Mechanisms consider domain constraints and participant incentives in real-world deployments. Within the theoretical foundations branch, a particularly active line of work investigates how different privacy definitions and noise mechanisms influence convergence rates under non-IID data and heterogeneous client participation. Convergent DP Federated[0] sits squarely in this cluster, analyzing the interplay between privacy guarantees and optimization convergence in federated settings. It shares thematic ground with Convergent fDP Perspective[9] and DP NonIID Convergence[8], which similarly examine convergence under differential privacy constraints and data heterogeneity, though each work may emphasize different noise calibration strategies or client sampling schemes. Nearby efforts such as DP Norm Primal Dual[3] and Harmonizing DP Mechanisms[4] explore alternative optimization frameworks and unified privacy accounting methods, highlighting ongoing questions about which algorithmic primitives best reconcile strong privacy with fast, stable learning. This landscape reveals a tension between tightening privacy bounds and maintaining practical convergence speeds, with Convergent DP Federated[0] contributing formal analysis that helps clarify these trade-offs in federated environments.

Claimed Contributions

Convergent privacy analysis for Noisy-FedAvg under non-convex objectives

The authors prove that the privacy budget in Noisy-FedAvg does not diverge as the number of communication rounds increases, achieving a convergent privacy bound for non-convex and smooth objectives. This is the first such convergent privacy analysis for FL-DP methods under non-convex functions.

9 retrieved papers
Convergent privacy analysis for Noisy-FedProx with constant lower bound

The authors demonstrate that the proximal regularization term in Noisy-FedProx enables privacy to converge to a stable constant lower bound, showing that well-designed local regularization can achieve both optimization and privacy benefits in FL-DP.

10 retrieved papers
f-DP based worst privacy evaluation framework using shifted interpolation

The authors develop a comprehensive framework for evaluating worst-case privacy in FL-DP methods by combining f-DP analysis with shifted interpolation techniques, providing information-theoretically lossless privacy bounds that can be converted to other DP frameworks.

4 retrieved papers

Core Task Comparisons

Comparisons with papers in the same taxonomy category

Contribution Analysis

Detailed comparisons for each claimed contribution

Contribution

Convergent privacy analysis for Noisy-FedAvg under non-convex objectives

The authors prove that the privacy budget in Noisy-FedAvg does not diverge as the number of communication rounds increases, achieving a convergent privacy bound for non-convex and smooth objectives. This is the first such convergent privacy analysis for FL-DP methods under non-convex functions.

Contribution

Convergent privacy analysis for Noisy-FedProx with constant lower bound

The authors demonstrate that the proximal regularization term in Noisy-FedProx enables privacy to converge to a stable constant lower bound, showing that well-designed local regularization can achieve both optimization and privacy benefits in FL-DP.

Contribution

f-DP based worst privacy evaluation framework using shifted interpolation

The authors develop a comprehensive framework for evaluating worst-case privacy in FL-DP methods by combining f-DP analysis with shifted interpolation techniques, providing information-theoretically lossless privacy bounds that can be converted to other DP frameworks.

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