# Representation-Aware Distributionally Robust Optimization: A Knowledge Transfer Framework

arXiv: https://arxiv.org/abs/2509.09371 · HTML: https://mlsanity.com/paper/2509.09371/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 24 of its 33 references that are in the map.
- First posted on arXiv 11 Sep 2025.

## Builds on (most cited first, 24 of 24)

- [Data-driven Distributionally Robust Optimization Using the Wasserstein Metric: Performance Guarantees and Tractable Reformulations](https://mlsanity.com/paper/1505.05116/) (2015)
- [Distributionally Robust Stochastic Optimization with Wasserstein Distance](https://mlsanity.com/paper/1604.02199/) (2016)
- [Distributionally Robust Logistic Regression](https://mlsanity.com/paper/1509.09259/) (2015)
- [Transfer Learning for High-dimensional Linear Regression: Prediction, Estimation, and Minimax Optimality](https://mlsanity.com/paper/2006.10593/) (2020)
- [Regularization via Mass Transportation](https://mlsanity.com/paper/1710.10016/) (2017)
- [Transfer Learning under High-dimensional Generalized Linear Models](https://mlsanity.com/paper/2105.14328/) (2021)
- [Finite-Sample Guarantees for Wasserstein Distributionally Robust Optimization: Breaking the Curse of Dimensionality](https://mlsanity.com/paper/2009.04382/) (2020)
- [Learning from Similar Linear Representations: Adaptivity, Minimaxity, and Robustness](https://mlsanity.com/paper/2303.17765/) (2023)
- [Statistical Analysis of Wasserstein Distributionally Robust Estimators](https://mlsanity.com/paper/2108.02120/) (2021)
- [Confidence Regions in Wasserstein Distributionally Robust Estimation](https://mlsanity.com/paper/1906.01614/) (2019)
- [Robust angle-based transfer learning in high dimensions](https://mlsanity.com/paper/2210.12759/) (2022)
- [Semi-supervised Triply Robust Inductive Transfer Learning](https://mlsanity.com/paper/2209.04977/) (2022)
- [TransFusion: Covariate-Shift Robust Transfer Learning for High-Dimensional Regression](https://mlsanity.com/paper/2404.01153/) (2024)
- [Domain Adaptation Optimized for Robustness in Mixture Populations](https://mlsanity.com/paper/2407.20073/) (2024)
- [Causality-oriented robustness: exploiting general noise interventions](https://mlsanity.com/paper/2307.10299/) (2023)
- [Domain Adaptation Targeting Heterogeneous and Imbalanced Subgroups](https://mlsanity.com/paper/2410.06484/) (2024)
- [On Regularized Square-root Regression Problems: Distributionally Robust Interpretation and Fast Computations](https://mlsanity.com/paper/2109.03632/) (2021)
- [Guided Adversarial Robust Transfer Learning with Source Mixing](https://mlsanity.com/paper/2309.06534/) (2023)
- [Distributionally robust risk evaluation with an isotonic constraint](https://mlsanity.com/paper/2407.06867/) (2024)
- [Knowledge-Guided Wasserstein Distributionally Robust Optimization](https://mlsanity.com/paper/2502.08146/) (2025)
- [Causality-Inspired Robustness for Nonlinear Models via Representation Learning](https://mlsanity.com/paper/2505.12868/) (2025)
- [Profiled Transfer Learning for High Dimensional Linear Model](https://mlsanity.com/paper/2406.00701/) (2024)
- [Wasserstein Distributionally Robust Optimization with Heterogeneous Data Sources](https://mlsanity.com/paper/2407.13582/) (2024)
- [Sufficiency-principled Transfer Learning via Model Averaging](https://mlsanity.com/paper/2507.15416/) (2025)

## Abstract (arXiv)

Distributionally robust optimization (DRO) protects statistical learning against distributional shifts by optimizing the worst-case performance over a set of perturbed distributions. However, standard DRO formulations often treat all feature perturbations equally. This can be unnecessarily conservative when external knowledge suggests that the predictive signal is embedded in a low-dimensional representation of covariates. We propose REpresentation-Aware Distributionally robust estimation (READ), a Wasserstein DRO framework that uses external representations to guide the geometry of robustness. Rather than uniformly perturbing all covariate directions, READ increases the transport cost of perturbations that change representation coordinates, thereby reshaping the dual regularization toward the representation subspace. Meanwhile, it preserves protection against variations orthogonal to the representation. We study READ in two regimes. First, for inference on the current target, we characterize our estimator asymptotically and develop a Wasserstein profile inference approach to construct representation-aligned confidence regions while enabling automatic hyperparameter tuning. Second, for deployment to future populations that differ from the current target but are generated from the same representation-invariant random-coefficient model, we show that the resulting regions achieve higher coverage of future model parameters than standard methods. Simulations and a single-cell multi-omics application demonstrate the advantages of READ in multi-source and multitask transfer learning settings.