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Specifying and Solving Robust Empirical Risk Minimization Problems Using CVXPY

Author

Listed:
  • Eric Luxenberg

    (Stanford University)

  • Dhruv Malik

    (Carnegie Mellon University)

  • Yuanzhi Li

    (Carnegie Mellon University)

  • Aarti Singh

    (Carnegie Mellon University)

  • Stephen Boyd

    (Stanford University)

Abstract

We consider robust empirical risk minimization (ERM), where model parameters are chosen to minimize the worst-case empirical loss when each data point varies over a given convex uncertainty set. In some simple cases, such problems can be expressed in an analytical form. In general the problem can be made tractable via dualization, which turns a min-max problem into a min-min problem. Dualization requires expertise and is tedious and error-prone. We demonstrate how CVXPY can be used to automate this dualization procedure in a user-friendly manner. Our framework allows practitioners to specify and solve robust ERM problems with a general class of convex losses, capturing many standard regression and classification problems. Users can easily specify any complex uncertainty set that is representable via disciplined convex programming (DCP) constraints.

Suggested Citation

  • Eric Luxenberg & Dhruv Malik & Yuanzhi Li & Aarti Singh & Stephen Boyd, 2024. "Specifying and Solving Robust Empirical Risk Minimization Problems Using CVXPY," Journal of Optimization Theory and Applications, Springer, vol. 202(3), pages 1158-1168, September.
    • Handle: RePEc:spr:joptap:v:202:y:2024:i:3:d:10.1007_s10957-024-02491-6
    DOI: 10.1007/s10957-024-02491-6
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