Differentially Private Gradient-Tracking-Based Distributed Stochastic Optimization over Directed Graphs

[2501.06793] Differentially Private Gradient-Tracking-Based Distributed Stochastic Optimization over Directed Graphs Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Electrical Engineering and Systems Science > Systems and Control arXiv:2501.06793 (eess) [Submitted on 12 Jan 2025 ( v1 ), last revised 14 Apr 2026 (this version, v6)] Title: Differentially Private Gradient-Tracking-Based Distributed Stochastic Optimization over Directed Graphs Authors: Jialong Chen , Jimin Wang , Ji-Feng Zhang View a PDF of the paper titled Differentially Private Gradient-Tracking-Based Distributed Stochastic Optimization over Directed Graphs, by Jialong Chen and 2 other authors View PDF HTML (experimental) Abstract: This paper proposes a differentially private gradient-tracking-based distributed stochastic optimization algorithm over directed graphs. In particular, privacy noises are incorporated into each agent's state and tracking variable to mitigate information leakage, after which the perturbed states and tracking variables are transmitted to neighbors. We design two novel schemes for the step-sizes and the sampling number within the algorithm. The sampling parameter-controlled subsampling method employed by both schemes enhances the differential privacy level, and ensures a finite cumulative privacy budget even over infinite iterations. The algorithm achieves both almost sure and mean square convergence for nonconvex objectives. Furthermore, when nonconvex objectives satisfy the Polyak-Lojasiewicz condition, Scheme (S1) achieves a polynomial mean square convergence rate, and Scheme (S2) achieves an exponential mean square convergence rate. The trade-off between privacy and convergence is presented. The effectiveness of the algorithm and its superior performance compared to existing works are illustrated through numerical examples of distributed training on the benchmark datasets "MNIST" and "CIFAR-10". Subjects: Systems and Control (eess.SY) Cite as: arXiv:2501.06793 [eess.SY] (or arXiv:2501.06793v6 [eess.SY] for this version) https://doi.org/10.48550/arXiv.2501.06793 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Jialong Chen [ view email ] [v1] Sun, 12 Jan 2025 12:10:42 UTC (434 KB) [v2] Mon, 14 Jul 2025 12:17:06 UTC (463 KB) [v3] Wed, 17 Dec 2025 06:30:15 UTC (554 KB) [v4] Wed, 24 Dec 2025 14:28:41 UTC (554 KB) [v5] Fri, 26 Dec 2025 02:57:24 UTC (554 KB) [v6] Tue, 14 Apr 2026 03:38:30 UTC (554 KB) Full-text links: Access Paper: View a PDF of the paper titled Differentially Private Gradient-Tracking-Based Distributed Stochastic Optimization over Directed Graphs, by Jialong Chen and 2 other authors View PDF HTML (experimental) TeX Source view license Current browse context: eess.SY < prev | next > new | recent | 2025-01 Change to browse by: cs cs.SY eess References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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