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Differentially Private Average Consensus with Improved Accuracy-Privacy Trade-off (2309.08464v3)

Published 15 Sep 2023 in eess.SY and cs.SY

Abstract: This paper studies the average consensus problem with differential privacy of initial states, for which it is widely recognized that there is a trade-off between the mean-square computation accuracy and privacy level. Considering the trade-off gap between the average consensus algorithm and the centralized averaging approach with differential privacy, we propose a distributed shuffling mechanism based on the Paillier cryptosystem to generate correlated zero-sum randomness. By randomizing each local privacy-sensitive initial state with an i.i.d. Gaussian noise and the output of the mechanism using Gaussian noises, it is shown that the resulting average consensus algorithm can eliminate the gap in the sense that the accuracy-privacy trade-off of the centralized averaging approach with differential privacy can be almost recovered by appropriately designing the variances of the added noises. We also extend such a design framework with Gaussian noises to the one using Laplace noises, and show that the improved privacy-accuracy trade-off is preserved.

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References (34)
  1. Z. Qiao, F. Guo, X. Pan, Y. Sun, and L. Wang, “Distributed load shedding via differentially private average consensus algorithm,” in 2022 34th Chinese Control and Decision Conference (CCDC), 2022, pp. 1503–1508.
  2. A. Nedić and J. Liu, “Distributed optimization for control,” Annual Review of Control, Robotics, and Autonomous Systems, vol. 1, pp. 77–103, 2018.
  3. T. Yang, X. Yi, J. Wu, Y. Yuan, D. Wu, Z. Meng, Y. Hong, H. Wang, Z. Lin, and K. H. Johansson, “A survey of distributed optimization,” Annual Reviews in Control, vol. 47, pp. 278–305, 2019.
  4. G. Shi, B. D. O. Anderson, and U. Helmke, “Network flows that solve linear equations,” IEEE Transactions on Automatic Control, vol. 62, no. 6, pp. 2659–2674, 2017.
  5. J. Lei, P. Yi, G. Shi, and B. D. O. Anderson, “Distributed algorithms with finite data rates that solve linear equations,” SIAM Journal on Optimization, vol. 30, no. 2, pp. 1191–1222, 2020.
  6. K. M. Lynch, I. B. Schwartz, P. Yang, and R. A. Freeman, “Decentralized environmental modeling by mobile sensor networks,” IEEE Transactions on Robotics, vol. 24, no. 3, pp. 710–724, 2008.
  7. H. Mortaji, S. H. Ow, M. Moghavvemi, and H. A. F. Almurib, “Load shedding and smart-direct load control using internet of things in smart grid demand response management,” IEEE Transactions on Industry Applications, vol. 53, no. 6, pp. 5155–5163, 2017.
  8. Z. Erkin, J. R. Troncoso-pastoriza, R. Lagendijk, and F. Perez-Gonzalez, “Privacy-preserving data aggregation in smart metering systems: an overview,” IEEE Signal Processing Magazine, vol. 30, no. 2, pp. 75–86, 2013.
  9. M. Ruan, H. Gao, and Y. Wang, “Secure and privacy-preserving consensus,” IEEE Transactions on Automatic Control, vol. 64, no. 10, pp. 4035–4049, 2019.
  10. N. M. Hung, Y.-U. Kim, and H.-S. Ahn, “A Novel Security Method for Exact Average Consensus,” IFAC-PapersOnLine, vol. 56, no. 2, pp. 8387–8392, 2023, 22nd IFAC World Congress.
  11. D. Calvaresi, M. Marinoni, A. Sturm, M. Schumacher, and G. Buttazzo, “The challenge of real-time multi-agent systems for enabling iot and cps,” in Proceedings of the International Conference on Web Intelligence.   New York, NY, USA: Association for Computing Machinery, 2017, p. 356–364.
  12. N. E. Manitara and C. N. Hadjicostis, “Privacy-preserving asymptotic average consensus,” in 2013 European Control Conference (ECC), 2013, pp. 760–765.
  13. C. Altafini, “A system-theoretic framework for privacy preservation in continuous-time multiagent dynamics,” Automatica, vol. 122, p. 109253, 2020.
  14. Y. Mo and R. M. Murray, “Privacy preserving average consensus,” IEEE Transactions on Automatic Control, vol. 62, no. 2, pp. 753–765, 2017.
  15. F. Farokhi and H. Sandberg, “Ensuring privacy with constrained additive noise by minimizing fisher information,” Automatica, vol. 99, pp. 275–288, 2019.
  16. C. Dwork, F. McSherry, K. Nissim, and A. Smith, “Calibrating noise to sensitivity in private data analysis,” in Theory of cryptography conference.   Springer, 2006, pp. 265–284.
  17. C. Dwork, A. Roth et al., “The algorithmic foundations of differential privacy.” Found. Trends Theor. Comput. Sci., vol. 9, no. 3-4, pp. 211–407, 2014.
  18. X. Yang, T. Wang, X. Ren, and W. Yu, “Survey on improving data utility in differentially private sequential data publishing,” IEEE Transactions on Big Data, vol. 7, no. 4, pp. 729–749, 2021.
  19. J. Le Ny and G. J. Pappas, “Differentially private filtering,” IEEE Transactions on Automatic Control, vol. 59, no. 2, pp. 341–354, 2013.
  20. Y. Kawano and M. Cao, “Design of privacy-preserving dynamic controllers,” IEEE Transactions on Automatic Control, vol. 65, no. 9, pp. 3863–3878, 2020.
  21. Y. Kawano, K. Kashima, and M. Cao, “Modular control under privacy protection: Fundamental trade-offs,” Automatica, vol. 127, p. 109518, 2021.
  22. K. Yazdani, A. Jones, K. Leahy, and M. Hale, “Differentially private lq control,” IEEE Transactions on Automatic Control, vol. 68, no. 2, pp. 1061–1068, 2022.
  23. S. Han, U. Topcu, and G. J. Pappas, “Differentially private distributed constrained optimization,” IEEE Transactions on Automatic Control, vol. 62, no. 1, pp. 50–64, 2016.
  24. E. Nozari, P. Tallapragada, and J. Cortés, “Differentially private distributed convex optimization via functional perturbation,” IEEE Transactions on Control of Network Systems, vol. 5, no. 1, pp. 395–408, 2016.
  25. Z. Huang, S. Mitra, and G. Dullerud, “Differentially private iterative synchronous consensus,” in Proceedings of the 2012 ACM Workshop on Privacy in the Electronic Society.   New York, NY, USA: Association for Computing Machinery, 2012, p. 81–90.
  26. E. Nozari, P. Tallapragada, and J. Cortés, “Differentially private average consensus: Obstructions, trade-offs, and optimal algorithm design,” Automatica, vol. 81, pp. 221–231, 2017.
  27. X.-K. Liu, J.-F. Zhang, and J. Wang, “Differentially private consensus algorithm for continuous-time heterogeneous multi-agent systems,” Automatica, vol. 122, p. 109283, 2020.
  28. L. Wang, I. R. Manchester, J. Trumpf, and G. Shi, “Differential initial-value privacy and observability of linear dynamical systems,” Automatica, vol. 148, p. 110722, 2023.
  29. J. He, L. Cai, and X. Guan, “Differential private noise adding mechanism and its application on consensus algorithm,” IEEE Transactions on Signal Processing, vol. 68, pp. 4069–4082, 2020.
  30. Y. Wang, “A Robust Dynamic Average Consensus Algorithm that Ensures both Differential Privacy and Accurate Convergence,” arXiv:2211.07791, 2023.
  31. B. Balle and Y.-X. Wang, “Improving the gaussian mechanism for differential privacy: Analytical calibration and optimal denoising,” in International Conference on Machine Learning.   PMLR, 2018, pp. 394–403.
  32. P. Paillier, “Public-key cryptosystems based on composite degree residuosity classes,” in International conference on the theory and applications of cryptographic techniques.   Springer, 1999, pp. 223–238.
  33. Q. Geng, W. Ding, R. Guo, and S. Kumar, “Tight Analysis of Privacy and Utility Tradeoff in Approximate Differential Privacy,” in Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics, ser. Proceedings of Machine Learning Research, S. Chiappa and R. Calandra, Eds., vol. 108.   PMLR, 26–28 Aug 2020, pp. 89–99.
  34. A. Nedic, A. Ozdaglar, and P. A. Parrilo, “Constrained consensus and optimization in multi-agent networks,” IEEE Transactions on Automatic Control, vol. 55, no. 4, pp. 922–938, 2010.
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