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Achievable Distributional Robustness When the Robust Risk Is Only Partially Identified by Kostin, Julia; Gnecco, Nicola; Yang, Fanny is a scholarly article available to read on EtoBox.

What is Achievable Distributional Robustness When the Robust Risk Is Only Partially Identified about?

In safety-critical applications, machine learning models should generalize well under worst-case distribution shifts, that is, have a small robust risk. Invariance-based algorithms can provably take advantage of structural assumptions on the shifts when the training distributions are heterogeneous enough to identify the robust risk. However, in practice, such identifiability conditions are rarely satisfied -- a scenario so far underexplored in the theoretical literature. In this paper, we aim to fill the gap and propose to study the more general setting when the robust risk is only partially identifiable. In particular, we introduce the worst-case robust risk as a new measure of robustness that is always well-defined regardless of identifiability. Its minimum corresponds to an algorithm-independent (population) minimax quantity that measures the best achievable robustness under partial identifiability. While these concepts can be defined more broadly, in this paper we introduce and derive them explicitly for a linear model for concreteness of the presentation. First, we show that existing robustness methods are provably suboptimal in the partially identifiable case. We then evaluat

Author

Kostin, Julia; Gnecco, Nicola; Yang, Fanny

Published

2025

Language

EN