Specifying and Solving Robust Empirical Risk Minimization Problems Using CVXPY

Eric Luxenberg (), Dhruv Malik (), Yuanzhi Li (), Aarti Singh () and Stephen Boyd ()
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Eric Luxenberg: Stanford University
Dhruv Malik: Carnegie Mellon University
Yuanzhi Li: Carnegie Mellon University
Aarti Singh: Carnegie Mellon University
Stephen Boyd: Stanford University

Journal of Optimization Theory and Applications, 2024, vol. 202, issue 3, No 7, 1158-1168

Abstract: 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.

Keywords: Robust optimization; Convex optimization; Empirical risk minimization; DCP; 90C25; 90C17; 90C47 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10957-024-02491-6

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