Structured Robustness for Distribution Shifts

Abstract

Out-of-distribution (OOD) data often undermines reliable model deployment in high-stakes domains such as financial markets, where overlooked correlations and unexpected shifts can render predictive systems ineffective. We propose STAR (Structured Transformations and Adversarial Reweighting), a framework that leverages the geometry of distribution shifts by combining transformation- based invariances with divergence-based robust optimization. Specifically, STAR places an f -divergence ball around each label-preserving transformation of the training sample, empowering an adversary to apply known transformations and reweight the resulting data within a specified divergence radius. This design cap- tures both large, structured shifts and subtle, unmodeled perturbations—a critical step toward mitigating shortcuts and spurious correlations. Notably, STAR recov- ers standard distributionally robust optimization if no structured transformations are assumed. We establish a uniform-convergence analysis showing that minimiz- ing STAR’s empirical nested min–max objective achieves low worst-case error over all admissible shifts with high probability. Our results quantify the additional samples needed to handle the adversary’s flexibility, providing theoretical guid- ance for selecting the divergence radius based on problem complexity. Empirical studies on synthetic and image benchmarks confirm that STAR outperforms base- lines, consistent with our theoretical findings.