Maximin Relative Improvement: Fair Learning as a Bargaining Problem

TL;DR

This paper introduces a game-theoretic approach to group fairness in machine learning, using bargaining solutions like Kalai-Smorodinsky to ensure scale-invariant and fair risk reduction across subpopulations.

Contribution

It proposes the concept of relative improvement for fair learning, connecting it to bargaining solutions and providing axiomatic justification and convergence guarantees.

Findings

Relative improvement aligns with Kalai-Smorodinsky solution.

Scale invariance addresses issues with different group predictability.

Finite-sample convergence guarantees are established.

Abstract

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.