# Statistical Analysis of Conditional Group Distributionally Robust Optimization with Cross-Entropy Loss

arXiv: https://arxiv.org/abs/2507.09905 · HTML: https://mlsanity.com/paper/2507.09905/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Jul 2025.

## Built on by (most cited first, 4 of 4)

- [Maximum Risk Minimization with Random Forests](https://mlsanity.com/paper/2512.10445/) (2025)
- [Robust Out-of-Distribution Stochastic Optimization](https://mlsanity.com/paper/2604.20147/) (2026)
- [Domain Adaptation with Target Information via Doubly-Anchored Distributionally Robust Optimization](https://mlsanity.com/paper/2609.32730/) (2026)
- [Guided Uncertainty-Aware Robust Domain Transfer](https://mlsanity.com/paper/2609.35654/) (2026)

## Abstract (arXiv)

In multi-source learning with discrete labels, distributional heterogeneity across domains poses a central challenge to developing predictive models that transfer reliably to unseen domains. We study multi-source unsupervised domain adaptation, where labeled data are available from multiple source domains and only unlabeled data are observed from the target domain. To address potential distribution shifts, we propose a novel Conditional Group Distributionally Robust Optimization (CG-DRO) framework that learns a classifier by minimizing the worst-case cross-entropy loss over the convex combinations of the conditional outcome distributions from sources domains. We develop an efficient Mirror Prox algorithm for solving the minimax problem and employ a double machine learning procedure to estimate the risk function, ensuring that errors in nuisance estimation contribute only at higher-order rates. We establish fast statistical convergence rates for the empirical CG-DRO estimator by constructing two surrogate minimax optimization problems that serve as theoretical bridges. A distinguishing challenge for CG-DRO is the emergence of nonstandard asymptotics: the empirical CG-DRO estimator may fail to converge to a standard limiting distribution due to boundary effects and system instability. To address this, we introduce a perturbation-based inference procedure that enables uniformly valid inference, including confidence interval construction and hypothesis testing.