Abstract
This paper considers the problem of releasing optimal power flow benchmarks that maintain the privacy of customers (loads) using the notion of Differential Privacy. It is motivated by the observation that traditional differential-privacy mechanisms are not accurate enough: The added noise fundamentally changes the nature of the underlying optimization and often leads to test cases with no solution. To remedy this limitation, the paper introduces the framework of Constraint-Based Differential Privacy (CBDP) that leverages the post- processing immunity of differential privacy to improve the accuracy of traditional mechanisms. More precisely, CBDP solves an optimization problem to satisfies the problem-specific constraints by redistributing the noise. The paper shows that CBDP enjoys desirable theoretical properties and produces orders of magnitude improvements on the largest set of test cases available.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
The experimental settings are reported in all details in Sect. 7.
References
Kaggle: Your home for data science. https://www.kaggle.com
Ács, G., Castelluccia, C.: I have a DREAM! (DiffeRentially privatE smArt Metering). In: Filler, T., Pevný, T., Craver, S., Ker, A. (eds.) IH 2011. LNCS, vol. 6958, pp. 118–132. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-24178-9_9
Andrés, M.E., Bordenabe, N.E., Chatzikokolakis, K., Palamidessi, C.: Geo-indistinguishability: differential privacy for location-based systems. In: Proceedings of the 2013 ACM SIGSAC Conference on Computer & Communications Security, pp. 901–914. ACM (2013)
Backes, M., Berrang, P., Hecksteden, A., Humbert, M., Keller, A., Meyer, T.: Privacy in epigenetics: temporal linkability of MicroRNA expression profiles. In: USENIX Security Symposium, pp. 1223–1240 (2016)
Dwork, C., McSherry, F., Nissim, K., Smith, A.: Calibrating noise to sensitivity in private data analysis. In: Halevi, S., Rabin, T. (eds.) TCC 2006. LNCS, vol. 3876, pp. 265–284. Springer, Heidelberg (2006). https://doi.org/10.1007/11681878_14
Dwork, C., Roth, A.: The algorithmic foundations of differential privacy. Theor. Comput. Sci. 9(3–4), 211–407 (2013)
Fanti, G., Pihur, V., Erlingsson, Ú.: Building a rappor with the unknown: privacy-preserving learning of associations and data dictionaries. Proc. Priv. Enhancing Technol. 2016(3), 41–61 (2016)
Fioretto, F., Lee, C., Van Hentenryck, P.: Constrained-based differential privacy for private mobility. In: Proceedings of the International Joint Conference on Autonomous Agents and Multiagent Systems (AAMAS) (2018)
Grainger, J.J.S., Grainger, W.D.J.J., Stevenson, W.D.: Power System Analysis. McGraw-Hill Education, New York City (1994)
Greenberg, A.: Apple’s ‘differential privacy’ is about collecting your data—but not your data, 13 June 2016. https://www.wired.com/2016/06/apples-differential-privacy-collecting-data/. Accessed 21 Sept 2016
Gurobi. Gurobi software. http://www.gurobi.com/
Hijazi, H., Coffrin, C., Van Hentenryck, P.: Convex quadratic relaxations of nonlinear programs in power systems. Math. Program. Comput. 32(5), 3549–3558 (2017)
IBM. ILOG CPLEX software. http://www.ibm.com/
Jabr, R.: Radial distribution load flow using conic programming. IEEE Trans. Power Syst. 21(3), 1458–1459 (2006)
Karapetyan, A., Azman, S.K., Aung, Z.: Assessing the privacy cost in centralized event-based demand response for microgrids. CoRR, abs/1703.02382 (2017)
Koufogiannis, F., Han, S., Pappas, G.J.: Optimality of the Laplace mechanism in differential privacy. arXiv preprint arXiv:1504.00065 (2015)
Lehmann, K., Grastien, A., Van Hentenryck, P.: AC-feasibility on tree networks is NP-hard. IEEE Trans. Power Syst. 99, 1–4 (2015)
Liao, X., Srinivasan, P., Formby, D., Beyah, A.R.: Di-PriDA: differentially private distributed load balancing control for the smart grid. IEEE Trans. Dependable Secure Comput. (2017). https://doi.org/10.1109/TDSC.2017.2717826
McCormick, G.: Computability of global solutions to factorable nonconvex programs: part i - convex underestimating problems. Math. Program. 10, 146–175 (1976)
Mir, D.J., Isaacman, S., Cáceres, R., Martonosi, M., Wright, R.N.: DP-WHERE: differentially private modeling of human mobility. In: 2013 IEEE International Conference on Big Data, pp. 580–588. IEEE (2013)
MOSEK ApS. The MOSEK optimization toolbox (2015)
Vadhan, S.: The complexity of differential privacy. Tutorials on the Foundations of Cryptography. ISC, pp. 347–450. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-57048-8_7
Verma, A.: Power grid security analysis: an optimization approach. Ph.D. thesis, Columbia University (2009)
Wood, A.J., Wollenberg, B.F.: Power Generation, Operation, and Control. Wiley, Hoboken (1996)
Zhao, J., Jung, T., Wang, Y., Li, X.: Achieving differential privacy of data disclosure in the smart grid. In: INFOCOM, 2014 Proceedings, pp. 504–512. IEEE (2014)
Acknowledgments
The authors would like to thank the anonymous reviewers for their valuable comments. This research is partly funded by the ARPA-E Grid Data Program under Grant 1357-1530. The views and conclusions contained in this document are those of the authors only.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG, part of Springer Nature
About this paper
Cite this paper
Fioretto, F., Van Hentenryck, P. (2018). Constrained-Based Differential Privacy: Releasing Optimal Power Flow Benchmarks Privately. In: van Hoeve, WJ. (eds) Integration of Constraint Programming, Artificial Intelligence, and Operations Research. CPAIOR 2018. Lecture Notes in Computer Science(), vol 10848. Springer, Cham. https://doi.org/10.1007/978-3-319-93031-2_15
Download citation
DOI: https://doi.org/10.1007/978-3-319-93031-2_15
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-93030-5
Online ISBN: 978-3-319-93031-2
eBook Packages: Computer ScienceComputer Science (R0)