General risk measures for robust machine learning
Mesures de risque générales pour l'apprentissage automatique robuste
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.
Origin : Files produced by the author(s)
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