1 / 26

Privacy-Preserving Linear Programming

Privacy-Preserving Linear Programming. UCSD – Center for Computational Mathematics Seminar January 11, 2011. Olvi Mangasarian UW Madison & UCSD La Jolla. TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: A A A A A A A A A A A A A A A. Problem Statement.

brooklyn
Download Presentation

Privacy-Preserving Linear Programming

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Privacy-Preserving Linear Programming UCSD – Center for Computational Mathematics Seminar January 11, 2011 Olvi Mangasarian UW Madison & UCSD La Jolla TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAAAAAAAAAA

  2. Problem Statement • Entities with related data wish to solve a linear program based on all the data • The entities are unwilling to reveal their data to each other • If each entity holds a different set of variables for all constraints, then the data is said to be vertically partitioned • If each entity holds a different set of constraints with all variables, then the data is said to be horizontally partitioned • Our approach: privacy-preserving linear programming (PPLP) using random matrix transformations • Provides exact solution to the total linear program • Does not reveal any private information

  3. Horizontally Partitioned Matrix Vertically Partitioned Matrix Linear Programming Constraint Matrix Variables 1 2 ..………….…………. n 1 2 ........m A A1 A¢1 A¢2 A¢3 Constraints A2 A3

  4. Outline • Vertically (horizontally) partitioned linear program • Secure transformation via a random matrix • Privacy-preserving linear program solution • Computational results • Summary

  5. A¢1 A¢2 A¢3 Vertically Partitioned Data:Each entity holds different variables for the same constraints A¢1 A¢2 A¢3

  6. LP with Vertically Partitioned Data We consider the linear program:

  7. Secure Linear Program Generation

  8. Why Secure Linear Program?

  9. Original & Secure LPs Are Equivalent

  10. PPLP Algorithm

  11. PPLP Algorithm (Continued)

  12. PPLP Algorithm (Continued)

  13. PPLP Algorithm (Continued)

  14. Computatinal ResultsExample 1 (k=n=1000)

  15. Computatinal ResultsExample 2 (k=n=100)

  16. A1 A2 A3 Horizontally Partitioned Constraint Matrix:Entities hold different constraints with the same variables A3 A1 A2

  17. LP with Horizontally Partitioned Data We consider the linear program:

  18. Secure Linear Program Generation

  19. Why Secure Linear Program?

  20. Original & Secure LPs Are Equivalent

  21. PPHPLP Algorithm

  22. PPHPLP Algorithm (Continued)

  23. Computatinal ResultsExample 1 (k=1000)

  24. Computatinal ResultsExample 2 (k=1000)

  25. Summary & Outlook • Based on a transformation using a random matrix B • Get exact solution to the original linear program without revealing privately held data Privacy preserving linear programming for vertically or horizontally partitioned data Possible extensions to: horizontally partitioned inequality constraints, complementarity problems and nonlinear programs

  26. References ftp://ftp.cs.wisc.edu/pub/dmi/tech-reports/10-01.pdf ftp://ftp.cs.wisc.edu/pub/dmi/tech-reports/10-02.pdf Optimization Letters, to appear

More Related