# Adaptive Sample-Level Framework Motivated by Distributionally Robust Optimization with Variance-Based Radius Assignment for Enhanced Neural Network Generalization Under Distribution Shift

arXiv: https://arxiv.org/abs/2511.05568 · HTML: https://mlsanity.com/paper/2511.05568/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 12 references that are in the map.
- First posted on arXiv 4 Nov 2025.

## Builds on (most cited first, 5 of 5)

- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Can You Trust Your Model's Uncertainty? Evaluating Predictive Uncertainty Under Dataset Shift](https://mlsanity.com/paper/1906.02530/) (2019)
- [Statistics of Robust Optimization: A Generalized Empirical Likelihood Approach](https://mlsanity.com/paper/1610.03425/) (2016)
- [Modeling the Second Player in Distributionally Robust Optimization](https://mlsanity.com/paper/2103.10282/) (2021)
- [Robust Distribution Learning with Local and Global Adversarial Corruptions](https://mlsanity.com/paper/2406.06509/) (2024)

## Abstract (arXiv)

Distribution shifts and minority subpopulations frequently undermine the reliability of deep neural networks trained using Empirical Risk Minimization (ERM). Distributionally Robust Optimization (DRO) addresses this by optimizing for the worst-case risk within a neighborhood of the training distribution. However, conventional methods depend on a single, global robustness budget, which can lead to overly conservative models or a misallocation of robustness. We propose a variance-driven, adaptive, sample-level DRO (Var-DRO) framework that automatically identifies high-risk training samples and assigns a personalized robustness budget to each based on its online loss variance. Our formulation employs two-sided, KL-divergence-style bounds to constrain the ratio between adversarial and empirical weights for every sample. This results in a linear inner maximization problem over a convex polytope, which admits an efficient water-filling solution. To stabilize training, we introduce a warmup phase and a linear ramp schedule for the global cap on per-sample budgets, complemented by label smoothing for numerical robustness. Evaluated on CIFAR-10-C (corruptions), our method achieves the highest overall mean accuracy compared to ERM and KL-DRO. On Waterbirds, Var-DRO improves overall performance while matching or surpassing KL-DRO. On the original CIFAR-10 dataset, Var-DRO remains competitive, exhibiting the modest trade-off anticipated when prioritizing robustness. The proposed framework is unsupervised (requiring no group labels), straightforward to implement, theoretically sound, and computationally efficient.