# An Axiomatic Theory of Provably-Fair Welfare-Centric Machine Learning

### Cyrus Cousins

## Abstract

We address an inherent difficulty in welfare-theoretic fair machine learning by proposing an equivalently axiomatically-justified alternative and studying the resulting computational and statistical learning questions. Welfare metrics quantify overall wellbeing across a population of one or more groups, and welfare-based objectives and constraints have recently been proposed to incentivize fair machine learning methods to produce satisfactory solutions that consider the diverse needs of multiple groups. Unfortunately, many machine-learning problems are more naturally cast as loss minimization tasks, rather than utility maximization, which complicates direct application of welfare-centric methods to fair machine learning. In this work, we define a complementary measure, termed malfare, measuring overall societal harm (rather than wellbeing), with axiomatic justification via the standard axioms of cardinal welfare. We then cast fair machine learning as malfare minimization over the risk values (expected losses) of each group. Surprisingly, the axioms of cardinal welfare (malfare) dictate that this is not equivalent to simply defining utility as negative loss. Building upon these concepts, we define fair-PAC learning, where a fair-PAC learner is an algorithm that learns an ε-δ malfare-optimal model with bounded sample complexity, for any data distribution, and for any (axiomatically justified) malfare concept. Finally, we show broad conditions under which, with appropriate modifications, standard PAC-learners may be converted to fair-PAC learners. This places fair-PAC learning on firm theoretical ground, as it yields statistical and computational efficiency guarantees for many well-studied machine-learning models, and is also practically relevant, as it democratizes fair machine learning by providing concrete training algorithms and rigorous generalization guarantees for these models.

## Keywords

Fair Machine Learning ♦ Cardinal Welfare Theory ♣ PAC-Learning ♥ Computational Learning Theory ♠ Statistical Learning Theory

Read the full paper on arXiv

Read the (deliciously concise) NeurIPS 2021 conference paper