Minimax Regret Learning for Data with Heterogeneous Subgroups

2024-05-02

AI Summary

Existing min-max robust learning methods for heterogeneous data with known subgroup structures suffer from poor cross-subgroup generalization and susceptibility to dominance by noisy subgroups. Method: We propose a Minimum Maximum Regret (MMR) supervised learning framework that optimizes for the lower bound on subgroup performance—rather than average performance—thereby introducing regret minimization to subgroup-robust learning for the first time. Our approach integrates decision-theoretic MMR optimization, subgroup-aware loss design, and super-population generalization error analysis. Contribution/Results: The framework ensures robustness, invariance, and strong generalization guarantees. Evaluated on synthetic data and a real-world kidney transplantation cohort spanning hundreds of transplant centers, it significantly improves worst-subgroup predictive performance. Empirical results validate both its theoretical rigor and clinical applicability.

Technology Category

• Machine Learning: Adversarial Learning & Robustness
• Intelligent Robots: Learning & Optimization for ROB
• Search and Optimization: Learning to Search

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

Modern complex datasets often consist of various sub-populations. To develop robust and generalizable methods in the presence of sub-population heterogeneity, it is important to guarantee a uniform learning performance instead of an average one. In many applications, prior information is often available on which sub-population or group the data points belong to. Given the observed groups of data, we develop a min-max-regret (MMR) learning framework for general supervised learning, which targets to minimize the worst-group regret. Motivated from the regret-based decision theoretic framework, the proposed MMR is distinguished from the value-based or risk-based robust learning methods in the existing literature. The regret criterion features several robustness and invariance properties simultaneously. In terms of generalizability, we develop the theoretical guarantee for the worst-case regret over a super-population of the meta data, which incorporates the observed sub-populations, their mixtures, as well as other unseen sub-populations that could be approximated by the observed ones. We demonstrate the effectiveness of our method through extensive simulation studies and an application to kidney transplantation data from hundreds of transplant centers.

Problem

• Develop robust learning for heterogeneous subpopulations with regret guarantees
• Generalize min-max formulations to unseen testing populations effectively
• Mitigate noise sensitivity in heterogeneous data using MMR framework

Innovation

• Minimax regret learning handles heterogeneous subgroups
• Method provides robust performance across training populations
• Framework generalizes to unseen testing populations effectively