# Stable Adversarial Learning under Distributional Shifts

arXiv: https://arxiv.org/abs/2006.04414 · HTML: https://mlsanity.com/paper/2006.04414/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Jun 2020.

## Built on by (most cited first, 16 of 16)

- [Towards Out-Of-Distribution Generalization: A Survey](https://mlsanity.com/paper/2108.13624/) (2021)
- [Rethinking the Evaluation Protocol of Domain Generalization](https://mlsanity.com/paper/2305.15253/) (2023)
- [Unified Group Fairness on Federated Learning](https://mlsanity.com/paper/2111.04986/) (2021)
- [Generalization Bounds with Minimal Dependency on Hypothesis Class via Distributionally Robust Optimization](https://mlsanity.com/paper/2106.11180/) (2021)
- [Moderately Distributional Exploration for Domain Generalization](https://mlsanity.com/paper/2304.13976/) (2023)
- [Supervision Adaptation Balancing In-distribution Generalization and Out-of-distribution Detection](https://mlsanity.com/paper/2206.09380/) (2022)
- [Exploiting Personalized Invariance for Better Out-of-distribution Generalization in Federated Learning](https://mlsanity.com/paper/2211.11243/) (2022)
- [Federated Distributionally Robust Optimization with Non-Convex Objectives: Algorithm and Analysis](https://mlsanity.com/paper/2307.14364/) (2023)
- [Treatment Learning Causal Transformer for Noisy Image Classification](https://mlsanity.com/paper/2203.15529/) (2022)
- [Graphs Generalization under Distribution Shifts](https://mlsanity.com/paper/2403.16334/) (2024)
- [Weighted Risk Invariance: Domain Generalization under Invariant Feature Shift](https://mlsanity.com/paper/2407.18428/) (2024)
- [Leveraging Robust Optimization for LLM Alignment under Distribution Shifts](https://mlsanity.com/paper/2504.05831/) (2025)
- [Invariant Random Forest: Tree-Based Model Solution for OOD Generalization](https://mlsanity.com/paper/2312.04273/) (2023)
- [Out-of-distribution materials property prediction using adversarial learning based fine-tuning](https://mlsanity.com/paper/2408.09297/) (2024)
- [DIRECT: Learning from Sparse and Shifting Rewards using Discriminative Reward Co-Training](https://mlsanity.com/paper/2301.07421/) (2023)
- [Data Heterogeneity Modeling for Trustworthy Machine Learning](https://mlsanity.com/paper/2506.00969/) (2025)

## Abstract (arXiv)

Machine learning algorithms with empirical risk minimization are vulnerable under distributional shifts due to the greedy adoption of all the correlations found in training data. Recently, there are robust learning methods aiming at this problem by minimizing the worst-case risk over an uncertainty set. However, they equally treat all covariates to form the decision sets regardless of the stability of their correlations with the target, resulting in the overwhelmingly large set and low confidence of the learner.In this paper, we propose Stable Adversarial Learning (SAL) algorithm that leverages heterogeneous data sources to construct a more practical uncertainty set and conduct differentiated robustness optimization, where covariates are differentiated according to the stability of their correlations with the target. We theoretically show that our method is tractable for stochastic gradient-based optimization and provide the performance guarantees for our method. Empirical studies on both simulation and real datasets validate the effectiveness of our method in terms of uniformly good performance across unknown distributional shifts.