Achievable distributional robustness when the robust risk is only partially identified

2025-02-04

AI Summary

In safety-critical settings, invariant learning methods yield suboptimal robustness when robust risk is only partially identifiable—due to insufficient heterogeneity across training environments. Method: We propose a well-defined worst-case robust risk as a novel robustness metric and formally define its population minimax optimum, characterizing the fundamental limit of robust generalization under partial identifiability. Within a linear model framework, we explicitly model this robust risk and minimize it empirically. Contribution/Results: We theoretically prove that standard invariance-based methods are inherently suboptimal in this regime. Empirical evaluation on real-world gene expression data demonstrates that our approach significantly improves out-of-distribution generalization—particularly as the proportion of unseen environments increases—thereby closing a critical gap between theoretical robustness guarantees and practical performance under limited environmental diversity.

Technology Category

• Machine Learning: Adversarial Learning & Robustness
• Natural Language Processing: Safety and Robustness
• Intelligent Robots: Learning & Optimization for ROB

Application Category

• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Security and Privacy: Large-scale security measurements
• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments

Abstract

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 evaluate these methods and the minimizer of the (empirical) worst-case robust risk on real-world gene expression data and find a similar trend: the test error of existing robustness methods grows increasingly suboptimal as the fraction of data from unseen environments increases, whereas accounting for partial identifiability allows for better generalization.

Problem

• Addresses robustness under partial risk identifiability.
• Introduces worst-case robust risk measure.
• Evaluates methods on real-world gene data.

Innovation

• Partial robust risk identification
• Worst-case robust risk measure
• Linear model empirical evaluation