# Distributionally Robust Optimization with Adversarial Data Contamination

arXiv: https://arxiv.org/abs/2507.10718 · HTML: https://mlsanity.com/paper/2507.10718/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 35 of its 52 references that are in the map.
- First posted on arXiv 14 Jul 2025.

## Builds on (most cited first, 30 of 35)

- [Just Train Twice: Improving Group Robustness without Training Group Information](https://mlsanity.com/paper/2107.09044/) (2021)
- [Sheared LLaMA: Accelerating Language Model Pre-training via Structured Pruning](https://mlsanity.com/paper/2310.06694/) (2023)
- [DoReMi: Optimizing Data Mixtures Speeds Up Language Model Pretraining](https://mlsanity.com/paper/2305.10429/) (2023)
- [Fairness Without Demographics in Repeated Loss Minimization](https://mlsanity.com/paper/1806.08010/) (2018)
- [Learning Models with Uniform Performance via Distributionally Robust Optimization](https://mlsanity.com/paper/1810.08750/) (2018)
- [Robust Estimators in High Dimensions without the Computational Intractability](https://mlsanity.com/paper/1604.06443/) (2016)
- [Distributionally Robust Stochastic Optimization with Wasserstein Distance](https://mlsanity.com/paper/1604.02199/) (2016)
- [Sever: A Robust Meta-Algorithm for Stochastic Optimization](https://mlsanity.com/paper/1803.02815/) (2018)
- [Regularization via Mass Transportation](https://mlsanity.com/paper/1710.10016/) (2017)
- [DORO: Distributional and Outlier Robust Optimization](https://mlsanity.com/paper/2106.06142/) (2021)
- [Towards Robust Alignment of Language Models: Distributionally Robustifying Direct Preference Optimization](https://mlsanity.com/paper/2407.07880/) (2024)
- [Outlier Robust Mean Estimation with Subgaussian Rates via Stability](https://mlsanity.com/paper/2007.15618/) (2020)
- [Finite-Sample Guarantees for Wasserstein Distributionally Robust Optimization: Breaking the Curse of Dimensionality](https://mlsanity.com/paper/2009.04382/) (2020)
- [Quantum Entropy Scoring for Fast Robust Mean Estimation and Improved Outlier Detection](https://mlsanity.com/paper/1906.11366/) (2019)
- [High-Dimensional Robust Mean Estimation in Nearly-Linear Time](https://mlsanity.com/paper/1811.09380/) (2018)
- [Generalized Resilience and Robust Statistics](https://mlsanity.com/paper/1909.08755/) (2019)
- [A Finite Sample Complexity Bound for Distributionally Robust Q-learning](https://mlsanity.com/paper/2302.13203/) (2023)
- [Doubly Robust Distributionally Robust Off-Policy Evaluation and Learning](https://mlsanity.com/paper/2202.09667/) (2022)
- [Optimal Transport Based Distributionally Robust Optimization: Structural Properties and Iterative Schemes](https://mlsanity.com/paper/1810.02403/) (2018)
- [Class-Weighted Classification: Trade-offs and Robust Approaches](https://mlsanity.com/paper/2005.12914/) (2020)
- [Robust Generalization against Photon-Limited Corruptions via Worst-Case Sharpness Minimization](https://mlsanity.com/paper/2303.13087/) (2023)
- [Outlier-Robust Optimal Transport: Duality, Structure, and Statistical Analysis](https://mlsanity.com/paper/2111.01361/) (2021)
- [Distributionally Robust Optimization and Robust Statistics](https://mlsanity.com/paper/2401.14655/) (2024)
- [Streaming Algorithms for High-Dimensional Robust Statistics](https://mlsanity.com/paper/2204.12399/) (2022)
- [Holistic Robust Data-Driven Decisions](https://mlsanity.com/paper/2207.09560/) (2022)
- [Distributionally Robust Model-based Reinforcement Learning with Large State Spaces](https://mlsanity.com/paper/2309.02236/) (2023)
- [Outlier-Robust Wasserstein DRO](https://mlsanity.com/paper/2311.05573/) (2023)
- [Robust Regression Revisited: Acceleration and Improved Estimation Rates](https://mlsanity.com/paper/2106.11938/) (2021)
- [Risk-Aware Planning and Assignment for Ground Vehicles using Uncertain Perception from Aerial Vehicles](https://mlsanity.com/paper/2003.11675/) (2020)
- [Fast Epigraphical Projection-based Incremental Algorithms for Wasserstein Distributionally Robust Support Vector Machine](https://mlsanity.com/paper/2010.12865/) (2020)

## Built on by (most cited first, 1 of 1)

- [Bulk-Calibrated Credal Ambiguity Sets: Fast, Tractable Decision Making under Out-of-Sample Contamination](https://mlsanity.com/paper/2601.21324/) (2026)

## Abstract (arXiv)

Distributionally Robust Optimization (DRO) provides a framework for decision-making under distributional uncertainty, yet its effectiveness can be compromised by outliers in the training data. This paper introduces a principled approach to simultaneously address both challenges. We focus on optimizing Wasserstein-1 DRO objectives for generalized linear models with convex Lipschitz loss functions, where an ε-fraction of the training data is adversarially corrupted. Our primary contribution lies in a novel modeling framework that integrates robustness against training data contamination with robustness against distributional shifts, alongside an efficient algorithm inspired by robust statistics to solve the resulting optimization problem. We prove that our method achieves an estimation error of O(√ε) for the true DRO objective value using only the contaminated data under the bounded covariance assumption. This work establishes the first rigorous guarantees, supported by efficient computation, for learning under the dual challenges of data contamination and distributional shifts.