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Robust Optimization and Applications in Machine Learning

Robust Optimization and Applications in Machine Learning. Laurent El Ghaoui SAC Capital and UC Berkeley elghaoui@eecs.berkeley.edu IMS Tutorial, N.U. Singapore, January 9, 2006. Thanks. Outline. Part 1: Overview of robust optimization. Optimization models. Pitfalls.

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Robust Optimization and Applications in Machine Learning

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  1. Robust Optimization andApplications in Machine Learning Laurent El Ghaoui SAC Capital and UC Berkeley elghaoui@eecs.berkeley.edu IMS Tutorial, N.U. Singapore, January 9, 2006

  2. Thanks

  3. Outline

  4. Part 1: Overview of robust optimization

  5. Optimization models

  6. Pitfalls

  7. Robust Optimization Paradigm

  8. Approximating a robust solution

  9. LP as a conic problem

  10. Second-order cone programming

  11. Semidefinite programming

  12. Dual form of conic program

  13. Robust conic programming

  14. Polytopic uncertainty

  15. Robust LP

  16. Robust LP with ellipsoidal uncertainty

  17. Robust LP as SOCP

  18. Example: robust portfolio design

  19. Solution of robust portfolio problem

  20. Robust SOCP

  21. Example: robust least-squares

  22. Robust SDP

  23. Example: robust control

  24. Analysis of robust conic problems

  25. Relaxations

  26. Quality estimates

  27. Quality estimates: some results

  28. Restriction

  29. Sampling

  30. Robust Optimization: challenges

  31. Robust optimization in machine learning

  32. Part 1: summary

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