可证明公平的福利中心机器学习公理化理论
An Axiomatic Theory of Provably-Fair Welfare-Centric Machine Learning
摘要：
我们解决了福利理论公平机器学习的固有困难，提出了一个等价的公理合理的替代方案，并研究由此产生的计算和统计学习问题。福利指标量化了一个或多个群体的总体福祉，最近提出了基于福利的目标和约束，以激励公平的机器学习方法，以产生考虑多个群体的不同需求的满意解决方案。不幸的是，许多机器学习问题更自然地被视为损失最小化任务，而不是效用最大化，这使得以福利为中心的方法直接应用于公平的机器学习变得复杂。在这项工作中，我们定义了一个补充措施，称为malfare，衡量整体社会危害（而不是福祉），通过基数福利的标准公理化的理由。然后，我们将公平的机器学习视为每组风险值（预期损失）的最小化。令人惊讶的是，基数福利（malfare）公理规定，这并不等同于简单地将效用定义为负损失。在这些概念的基础上，我们定义了公平PAC（FPAC）学习，其中FPAC学习器是一种算法，学习$\varepsilon$ - $δ$ malfare最优模型，具有有限的样本复杂度，任何数据分布，并为任何（公理合理）malfare概念。最后，我们展示了广泛的条件，在此条件下，经过适当的修改，标准PAC学习者可以转换为FPAC学习者。这将FPAC学习置于坚实的理论基础之上，因为它为许多经过充分研究的机器学习模型提供了统计和计算效率保证，并且也具有实际意义，因为它通过为这些模型提供具体的训练算法和严格的泛化保证，使公平ML民主化
英文摘要：
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 (FPAC) learning, where an FPAC learner is an algorithm that learns an $\varepsilon$-$δ$ 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 FPAC learners. This places FPAC 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 ML by providing concrete training algorithms and rigorous generalization guarantees for these models
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