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We address an inherent difficulty in welfare-theoretic fair machine learningby proposing an equivalently axiomatically-justified alternative and studyingthe resulting computational and statistical learning questions. Welfare metricsquantify overall wellbeing across a population of one or more groups, andwelfare-based objectives and constraints have recently been proposed toincentivize fair machine learning methods to produce satisfactory solutionsthat consider the diverse needs of multiple groups. Unfortunately, manymachine-learning problems are more naturally cast as loss minimization tasks,rather than utility maximization, which complicates direct application ofwelfare-centric methods to fair machine learning. In this work, we define acomplementary measure, termed malfare, measuring overall societal harm (ratherthan wellbeing), with axiomatic justification via the standard axioms ofcardinal welfare. We then cast fair machine learning as malfare minimizationover the risk values (expected losses) of each group. Surprisingly, the axiomsof cardinal welfare (malfare) dictate that this is not equivalent to simplydefining utility as negative loss. Building upon these concepts, we definefair-PAC (FPAC) learning, where an FPAC learner is an algorithm that learns an$\varepsilon$-$\delta$ malfare-optimal model with bounded sample complexity,for any data distribution, and for any (axiomatically justified) malfareconcept. Finally, we show broad conditions under which, with appropriatemodifications, standard PAC-learners may be converted to FPAC learners. Thisplaces FPAC learning on firm theoretical ground, as it yields statistical andcomputational efficiency guarantees for many well-studied machine-learningmodels, and is also practically relevant, as it democratizes fair ML byproviding concrete training algorithms and rigorous generalization guaranteesfor these models

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