# Specifying and Solving Robust Empirical Risk Minimization Problems Using CVXPY

arXiv: https://arxiv.org/abs/2306.05649 · HTML: https://mlsanity.com/paper/2306.05649/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 13 references that are in the map.
- First posted on arXiv 9 Jun 2023.

## Builds on (most cited first, 4 of 4)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [CVXPY: A Python-Embedded Modeling Language for Convex Optimization](https://mlsanity.com/paper/1603.00943/) (2016)
- [Disciplined Saddle Programming](https://mlsanity.com/paper/2301.13427/) (2023)
- [RIGID: Robust Linear Regression with Missing Data](https://mlsanity.com/paper/2205.13635/) (2022)

## Abstract (arXiv)

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.