# Minimax Regret Learning for Data with Heterogeneous Subgroups

arXiv: https://arxiv.org/abs/2405.01709 · HTML: https://mlsanity.com/paper/2405.01709/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 58 references that are in the map.
- First posted on arXiv 2 May 2024.

## Builds on (most cited first, 21 of 21)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [WILDS: A Benchmark of in-the-Wild Distribution Shifts](https://mlsanity.com/paper/2012.07421/) (2020)
- [Distributionally Robust Neural Networks for Group Shifts: On the Importance of Regularization for Worst-Case Generalization](https://mlsanity.com/paper/1911.08731/) (2019)
- [SemEval-2017 Task 1: Semantic Textual Similarity - Multilingual and Cross-lingual Focused Evaluation](https://mlsanity.com/paper/1708.00055/) (2017)
- [Convex Optimization: Algorithms and Complexity](https://mlsanity.com/paper/1405.4980/) (2014)
- [Causal inference using invariant prediction: identification and confidence intervals](https://mlsanity.com/paper/1501.01332/) (2015)
- [Confounding variables can degrade generalization performance of radiological deep learning models](https://mlsanity.com/paper/1807.00431/) (2018)
- [Demographic Dialectal Variation in Social Media: A Case Study of African-American English](https://mlsanity.com/paper/1608.08868/) (2016)
- [Transfer Learning for High-dimensional Linear Regression: Prediction, Estimation, and Minimax Optimality](https://mlsanity.com/paper/2006.10593/) (2020)
- [Feature Robustness in Non-stationary Health Records: Caveats to Deployable Model Performance in Common Clinical Machine Learning Tasks](https://mlsanity.com/paper/1908.00690/) (2019)
- [Distribution-Free Prediction Sets for Two-Layer Hierarchical Models](https://mlsanity.com/paper/1809.07441/) (2018)
- [Maximin effects in inhomogeneous large-scale data](https://mlsanity.com/paper/1406.0596/) (2014)
- [Minimax Regret Optimization for Robust Machine Learning under Distribution Shift](https://mlsanity.com/paper/2202.05436/) (2022)
- [Learning Optimal Distributionally Robust Individualized Treatment Rules](https://mlsanity.com/paper/2006.15121/) (2020)
- [Environment Invariant Linear Least Squares](https://mlsanity.com/paper/2303.03092/) (2023)
- [Statistical Inference for Maximin Effects: Identifying Stable Associations across Multiple Studies](https://mlsanity.com/paper/2011.07568/) (2020)
- [Methods for Integrating Trials and Non-Experimental Data to Examine Treatment Effect Heterogeneity](https://mlsanity.com/paper/2302.13428/) (2023)
- [Policy Learning under Biased Sample Selection](https://mlsanity.com/paper/2304.11735/) (2023)
- [Individualized Decision-Making Under Partial Identification: Three Perspectives, Two Optimality Results, and One Paradox](https://mlsanity.com/paper/2110.10961/) (2021)

## Built on by (most cited first, 7 of 7)

- [Minimax Regret Estimation for Generalizing Heterogeneous Treatment Effects with Multisite Data](https://mlsanity.com/paper/2412.11136/) (2024)
- [Maximum Risk Minimization with Random Forests](https://mlsanity.com/paper/2512.10445/) (2025)
- [Adversarial Drift-Aware Predictive Transfer: Toward Durable Clinical AI](https://mlsanity.com/paper/2601.11860/) (2026)
- [Maximin Relative Improvement: Fair Learning as a Bargaining Problem](https://mlsanity.com/paper/2602.04155/) (2026)
- [Maximin Learning of Individualized Treatment Effect on Multi-Domain Outcomes](https://mlsanity.com/paper/2603.27114/) (2026)
- [CVaR anchor regression protects against rare shifts](https://mlsanity.com/paper/2609.27034/) (2026)
- [Guided Uncertainty-Aware Robust Domain Transfer](https://mlsanity.com/paper/2609.35654/) (2026)

## Abstract (arXiv)

Modern complex datasets often consist of various sub-populations with known group information. In the presence of sub-population heterogeneity, it is crucial to develop robust and generalizable learning methods that (1) can enjoy robust performance on each of the training populations, and (2) is generalizable to an unseen testing population. While various min-max formulations have been proposed to achieve (1) in the robust learning literature, their generalization to an unseen testing is less explored. Moreover, a general min-max formulation can be sensitive to the noise heterogeneity, and, in the extreme case, be degenerate such that a single high-noise population dominates. The min-max-regret (MMR) can mitigate these challenges. In this work, we consider a distribution-free robust hierarchical model for the generalization from multiple training populations to an unseen testing population. Under the robust hierarchical model, the empirical MMR can enjoy the regret guarantees on each of the training populations as well as the unseen testing population. We further specialize the general MMR framework to linear regression and generalized linear model, where we characterize the geometry of MMR and its distinction from other robust methods. We demonstrate the effectiveness of MMR through extensive simulation studies and an application to image recognition.