# General risk measures for robust machine learning

## TL;DR

This paper introduces a novel framework for robust machine learning by applying risk measures from quantitative finance, transforming min-max problems into convex optimization problems with practical algorithms and demonstrating their effectiveness on real data.

## Contribution

It adapts risk measure frameworks to machine learning, providing convex reformulations and efficient algorithms for robust models under distributional uncertainty.

## Key findings

- Convex reformulation of min-max problems under certain assumptions
- Development of an efficient algorithm for complex convex constraints
- Successful scaling of the algorithm on real datasets

## Abstract

A wide array of machine learning problems are formulated as the minimization of the expectation of a convex loss function on some parameter space. Since the probability distribution of the data of interest is usually unknown, it is is often estimated from training sets, which may lead to poor out-of-sample performance. In this work, we bring new insights in this problem by using the framework which has been developed in quantitative finance for risk measures. We show that the original min-max problem can be recast as a convex minimization problem under suitable assumptions. We discuss several important examples of robust formulations, in particular by defining ambiguity sets based on $\varphi$-divergences and the Wasserstein metric.We also propose an efficient algorithm for solving the corresponding convex optimization problems involving complex convex constraints. Through simulation examples, we demonstrate that this algorithm scales well on real data sets.