Papers
Topics
Authors
Recent
Search
2000 character limit reached

Design of Stochastic Quantizers for Privacy Preservation

Published 5 Mar 2024 in eess.SY, cs.CR, and cs.SY | (2403.03048v1)

Abstract: In this paper, we examine the role of stochastic quantizers for privacy preservation. We first employ a static stochastic quantizer and investigate its corresponding privacy-preserving properties. Specifically, we demonstrate that a sufficiently large quantization step guarantees $(0, \delta)$ differential privacy. Additionally, the degradation of control performance caused by quantization is evaluated as the tracking error of output regulation. These two analyses characterize the trade-off between privacy and control performance, determined by the quantization step. This insight enables us to use quantization intentionally as a means to achieve the seemingly conflicting two goals of maintaining control performance and preserving privacy at the same time; towards this end, we further investigate a dynamic stochastic quantizer. Under a stability assumption, the dynamic stochastic quantizer can enhance privacy, more than the static one, while achieving the same control performance. We further handle the unstable case by additionally applying input Gaussian noise.

Authors (3)
Definition Search Book Streamline Icon: https://streamlinehq.com
References (34)
  1. G. Wang, B. Wang, T. Wang, A. Nika, H. Zheng, and B. Y. Zhao, “Defending against sybil devices in crowdsourced mapping services,” in Proceedings of 14th Annual International Conference on Mobile Systems, Applications, and Services, pp. 179–191, 2016.
  2. R. Tourani, S. Misra, T. Mick, and G. Panwar, “Security, privacy, and access control in information-centric networking: A survey,” IEEE communications surveys & tutorials, vol. 20, no. 1, pp. 566–600, 2017.
  3. J. Cortés, G. E. Dullerud, S. Han, J. Le Ny, S. Mitra, and G. J. Pappas, “Differential privacy in control and network systems,” in 55th IEEE Conference on Decision and Control, pp. 4252–4272, 2016.
  4. Y. Mo and R. M. Murray, “Privacy preserving average consensus,” IEEE Transactions on Automatic Control, vol. 62, no. 2, pp. 753–765, 2016.
  5. C. Hawkins and M. Hale, “Differentially private formation control: Privacy and network co-design,” arXiv preprint arXiv:2205.13406, 2022.
  6. 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.
  7. K. Zhang, Z. Li, Y. Wang, and N. Li, “Privacy-preserved nonlinear cloud-based model predictive control via affine masking,” arXiv preprint arXiv:2112.10625, 2021.
  8. F. Fagnani and S. Zampieri, “Quantized stabilization of linear systems: complexity versus performance,” IEEE Transactions on Automatic Control, vol. 49, no. 9, pp. 1534–1548, 2004.
  9. H. Liang, Y. Zhang, T. Huang, and H. Ma, “Prescribed performance cooperative control for multiagent systems with input quantization,” IEEE Transactions on Cybernetics, vol. 50, no. 5, pp. 1810–1819, 2020.
  10. L. N. Bikas and G. A. Rovithakis, “Tracking performance guarantees in the presence of quantization for uncertain nonlinear systems,” IEEE Transactions on Automatic Control, vol. 66, no. 7, pp. 3311–3316, 2021.
  11. C. Murguia, I. Shames, F. Farokhi, and D. Nešić, “On privacy of quantized sensor measurements through additive noise,” in 57th IEEE Conference on Decision and Control, pp. 2531–2536, IEEE, 2018.
  12. Y. Kawano and M. Cao, “Effects of quantization and dithering in privacy analysis for a networked control system,” in 60th IEEE Conference on Decision and Control, pp. 2758–2763, 2021.
  13. X. Bu, P. Zhu, Q. Yu, Z. Hou, and J. Liang, “Model-free adaptive control for a class of nonlinear systems with uniform quantizer,” International Journal of Robust and Nonlinear Control, vol. 30, no. 16, pp. 6383–6398, 2020.
  14. B. Li, Z. Wang, Q.-L. Han, and H. Liu, “Distributed quasiconsensus control for stochastic multiagent systems under round-robin protocol and uniform quantization,” IEEE Transactions on Cybernetics, vol. 52, no. 7, pp. 6721–6732, 2020.
  15. M. Fu and L. Xie, “The sector bound approach to quantized feedback control,” IEEE Transactions on Automatic Control, vol. 50, no. 11, pp. 1698–1711, 2005.
  16. R. Brockett and D. Liberzon, “Quantized feedback stabilization of linear systems,” IEEE Transactions on Automatic Control, vol. 45, no. 7, pp. 1279–1289, 2000.
  17. D. Liberzon, “Hybrid feedback stabilization of systems with quantized signals,” Automatica, vol. 39, no. 9, pp. 1543–1554, 2003.
  18. D. Liberzon, “Quantization, time delays, and nonlinear stabilization,” IEEE Transactions on Automatic Control, vol. 51, no. 7, pp. 1190–1195, 2006.
  19. C. Dwork, “Differential privacy,” in International Colloquium on Automata, Languages, and Programming, pp. 1–12, Springer, 2006.
  20. S. Asoodeh, M. Aliakbarpour, and F. P. Calmon, “Local differential privacy is equivalent to contraction of an f𝑓fitalic_f-divergence,” in 2021 IEEE International Symposium on Information Theory (ISIT), pp. 545–550, 2021.
  21. Y. Zhao and J. Chen, “A survey on differential privacy for unstructured data content,” ACM Computing Surveys (CSUR), vol. 54, no. 10s, pp. 1–28, 2022.
  22. L. Liu, Y. Kawano, and M. Cao, “Privacy analysis for quantized networked control systems,” in 62nd IEEE Conference on Decision and Control (CDC), pp. 5073–5078, IEEE, 2023.
  23. Y. Wang and T. Başar, “Quantization enabled privacy protection in decentralized stochastic optimization,” IEEE Transactions on Automatic Control, vol. 68, no. 7, pp. 4038–4052, 2023.
  24. X. Duan, J. He, P. Cheng, Y. Mo, and J. Chen, “Privacy preserving maximum consensus,” in 54th IEEE Conference on Decision and Control, pp. 4517–4522, 2015.
  25. 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.
  26. C. Altafini, “A dynamical approach to privacy preserving average consensus,” in 58th IEEE Conference on Decision and Control, pp. 4501–4506, IEEE, 2019.
  27. Y. Wang, “Privacy-preserving average consensus via state decomposition,” IEEE Transactions on Automatic Control, vol. 64, no. 11, pp. 4711–4716, 2019.
  28. Y. Kawano and M. Cao, “Design of privacy-preserving dynamic controllers,” IEEE Transactions on Automatic Control, vol. 65, no. 9, pp. 3863–3878, 2020.
  29. 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.
  30. J. Huang, Nonlinear Output Regulation: Theory and Applications. SIAM, 2004.
  31. F. Fagnani and S. Zampieri, “Stability analysis and synthesis for scalar linear systems with a quantized feedback,” IEEE Transactions on automatic control, vol. 48, no. 9, pp. 1569–1584, 2003.
  32. C. Liverani, “Decay of correlations for piecewise expanding maps,” Journal of Statistical Physics, vol. 78, pp. 1111–1129, 1995.
  33. J. Buzzi, “Intrinsic ergodicity of affine maps in [0, 1] d,” Monatshefte für Mathematik, vol. 124, pp. 97–118, 1997.
  34. J. Le Ny and G. J. Pappas, “Differentially private filtering,” IEEE Transactions on Automatic Control, vol. 59, no. 2, pp. 341–354, 2014.

Summary

No one has generated a summary of this paper yet.

Sign Up to Summarize

Paper to Video (Beta)

No one has generated a video about this paper yet.

Sign Up to Generate All Videos Subscribe on YouTube

Whiteboard

No one has generated a whiteboard explanation for this paper yet.

Sign Up to Generate

Open Problems

We haven't generated a list of open problems mentioned in this paper yet.

Generate Now

Continue Learning

We haven't generated follow-up questions for this paper yet.

Generate Now

Collections

Sign up for free to add this paper to one or more collections.

Sign Up