mlsanityData to 14 Oct 2026

Differential Privacy for Euclidean Jordan Algebra with Applications to Private Symmetric Cone Programming

arXiv 2509.16915 ↗First posted 21 Sep 2025math.OC cs.CR cs.DScited by 0

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Abstract (arXiv)

In this paper, we study differentially private mechanisms for functions whose outputs lie in a Euclidean Jordan algebra. Euclidean Jordan algebras capture many important mathematical structures and form the foundation of linear programming, second-order cone programming, and semidefinite programming. Our main contribution is a generic Gaussian mechanism for such functions, with sensitivity measured in ℓ2, ℓ1, and ℓ_∞ norms. Notably, this framework includes the important case where the function outputs are symmetric matrices, and sensitivity is measured in the Frobenius, nuclear, or spectral norm. We further derive private algorithms for solving symmetric cone programs under various settings, using a combination of the multiplicative weights update method and our generic Gaussian mechanism. As an application, we present differentially private algorithms for semidefinite programming, resolving a major open question posed by [Hsu, Roth, Roughgarden, and Ullman, ICALP 2014].

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References · 34

  1. 2016Deep Learning with Differential Privacycited by 2,728
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  3. 2017Differentially Private Federated Learning: A Client Level Perspectivecited by 459
  4. 2019Differential Privacy Has Disparate Impact on Model Accuracycited by 316
  5. 2018Subsampled R'enyi Differential Privacy and Analytical Moments Accountantcited by 236
  6. 2019Differentially Private Learning with Adaptive Clippingcited by 220
  7. 2018Improving the Gaussian Mechanism for Differential Privacy: Analytical Calibration and Optimal Denoisingcited by 218
  8. 2020LDP-Fed: Federated Learning with Local Differential Privacycited by 132
  9. 2021Differential Privacy for Text Analytics via Natural Text Sanitizationcited by 77
  10. 2021Differentially Private Federated Learning on Heterogeneous Datacited by 74
  11. 2018High-Dimensional Robust Mean Estimation in Nearly-Linear Timecited by 39
  12. 2023Low Rank Matrix Completion via Robust Alternating Minimization in Nearly Linear Timecited by 31
22 more
  1. 2019Faster Algorithms for High-Dimensional Robust Covariance Estimationcited by 28
  2. 2022Sketching for First Order Method: Efficient Algorithm for Low-Bandwidth Channel and Vulnerabilitycited by 25
  3. 2022Sketching Meets Differential Privacy: Fast Algorithm for Dynamic Kronecker Projection Maintenancecited by 22
  4. 2018SynTF: Synthetic and Differentially Private Term Frequency Vectors for Privacy-Preserving Text Miningcited by 21
  5. 2020Adversarially Robust Streaming Algorithms via Differential Privacycited by 21
  6. 2017Near-Optimal Discrete Optimization for Experimental Design: A Regret Minimization Approachcited by 19
  7. 2021Dynamic Algorithms Against an Adaptive Adversary: Generic Constructions and Lower Boundscited by 17
  8. 2023Faster Algorithms for Structured Linear and Kernel Support Vector Machinescited by 13
  9. 2021A Framework for Adversarial Streaming via Differential Privacy and Difference Estimatorscited by 9
  10. 2023Efficient Alternating Minimization with Applications to Weighted Low Rank Approximationcited by 9
  11. 2014Privately Solving Linear Programscited by 7
  12. 2022DPAUC: Differentially Private AUC Computation in Federated Learningcited by 7
  13. 2023Robust Algorithms on Adaptive Inputs from Bounded Adversariescited by 5
  14. 2023Matrix Completion in Almost-Verification Timecited by 4
  15. 2017Matrix Completion from O(n) Samples in Linear Timecited by 3
  16. 2020Private Optimization Without Constraint Violationscited by 3
  17. 2020Differentially Private Convex Optimization with Feasibility Guaranteescited by 2
  18. 2024A Primal-Dual Framework for Symmetric Cone Programmingcited by 2
  19. 2024Guaranteed Feasibility in Differentially Private Linearly Constrained Convex Optimizationcited by 2
  20. 2020A geodesic interior-point method for linear optimization over symmetric conescited by 1
  21. 2025Differentially Private Linear Programming: Reduced Sub-Optimality and Guaranteed Constraint Satisfactioncited by 1
  22. 2025On Differential Privacy for Adaptively Solving Search Problems via Sketchingcited by 1

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