Maximin Relative Improvement: Fair Learning as a Bargaining Problem
This addresses fairness in deploying predictors across multiple subpopulations, offering a novel game-theoretic perspective that is not incremental.
The paper tackles the problem of group fairness in machine learning by framing it as a bargaining problem among subpopulations, proposing relative improvement as a method that recovers the Kalai-Smorodinsky solution and provides axiomatic justification with finite-sample convergence guarantees.
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.