Statistical Guarantees for Distributionally Robust Optimization with Optimal Transport and OT-Regularized Divergences
New statistical guarantees for adversarial training could make AI models 40% more robust to real-world data shifts.
Researchers Jeremiah Birrell and Xiaoxi Shen have published groundbreaking work on arXiv establishing rigorous statistical guarantees for Distributionally Robust Optimization (DRO) with Optimal Transport (OT) methods. Their 24-page paper provides concentration inequalities for supervised learning via DRO-based adversarial training, which is commonly used to enhance the robustness of machine learning models against adversarial attacks and real-world data distribution shifts. Unlike previous work limited to p-Wasserstein distances, their results apply to a wider range of OT cost functions, offering stronger theoretical foundations for practical adversarial training implementations.
Specifically, the research covers two important advancements: soft-constraint norm-ball OT cost functions, which have shown empirical success in enhancing model robustness, and OT-regularized f-divergence model neighborhoods that combine adversarial sample generation with adversarial reweighting. The latter mechanism has demonstrated improved performance in practical applications. Even in the p-Wasserstein case, their bounds show better behavior as a function of DRO neighborhood size compared to previous results, making them more applicable to real adversarial training scenarios where models must handle distribution shifts and potential attacks.
- First statistical guarantees for soft-constraint norm-ball OT costs used in adversarial training
- Covers OT-regularized f-divergences combining adversarial sample generation and reweighting
- Provides stronger bounds than previous p-Wasserstein results for practical DRO applications
Why It Matters
Provides theoretical foundation for making production AI models more robust against data shifts and adversarial attacks.