No-Free-Fairness: Fundamental Limits and Trade-offs in Learning Systems

The paper presents the No-Free-Fairness theorems, which establish fundamental limits on achieving fairness in learning systems. It identifies three sources of disparity: the trade-off between performance and fairness due to irreducible subgroup costs, the nontrivial subgroup disparity arising from finite-sample learning in ideal settings, and the limitations of model expressivity that prevent fair outcomes. These findings emphasize that fairness in AI systems cannot be solely addressed through data bias or optimization strategies, but must be considered as a core design challenge that involves explicit trade-offs.