# Maximin Relative Improvement: Fair Learning as a Bargaining Problem

arXiv: https://arxiv.org/abs/2602.04155 · HTML: https://mlsanity.com/paper/2602.04155/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 35 references that are in the map.
- First posted on arXiv 4 Feb 2026.

## Builds on (most cited first, 11 of 11)

- [Equality of Opportunity in Supervised Learning](https://mlsanity.com/paper/1610.02413/) (2016)
- [Distributionally Robust Neural Networks for Group Shifts: On the Importance of Regularization for Worst-Case Generalization](https://mlsanity.com/paper/1911.08731/) (2019)
- [A Reductions Approach to Fair Classification](https://mlsanity.com/paper/1803.02453/) (2018)
- [Retiring Adult: New Datasets for Fair Machine Learning](https://mlsanity.com/paper/2108.04884/) (2021)
- [Fair Regression: Quantitative Definitions and Reduction-based Algorithms](https://mlsanity.com/paper/1905.12843/) (2019)
- [Minimax Pareto Fairness: A Multi Objective Perspective](https://mlsanity.com/paper/2011.01821/) (2020)
- [From Parity to Preference-based Notions of Fairness in Classification](https://mlsanity.com/paper/1707.00010/) (2017)
- [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)
- [Does enforcing fairness mitigate biases caused by subpopulation shift?](https://mlsanity.com/paper/2011.03173/) (2020)
- [Minimax Regret Learning for Data with Heterogeneous Subgroups](https://mlsanity.com/paper/2405.01709/) (2024)

## Abstract (arXiv)

When deploying a single predictor across multiple subpopulations, we propose a fundamentally different approach: interpreting group fairness as a bargaining problem among subpopulations. This game-theoretic perspective reveals that existing robust optimization methods such as minimizing worst-group loss or regret correspond to classical bargaining solutions and embody different fairness principles. We propose relative improvement, the ratio of actual risk reduction to potential reduction from a baseline predictor, which recovers the Kalai-Smorodinsky solution. Unlike absolute-scale methods that may not be comparable when groups have different potential predictability, relative improvement provides axiomatic justification including scale invariance and individual monotonicity. We establish finite-sample convergence guarantees under mild conditions.