This paper introduces a framework for estimating fair optimal predictions using machine learning where the notion of fairness can be quantified using path-specific causal effects. We use a recently developed approach based on Lagrange multipliers for infinite-dimensional functional estimation to derive closed-form solutions for constrained optimization based on mean squared error and cross-entropy risk criteria. The theoretical forms of the solutions are analyzed in detail and described as nuanced adjustments to the unconstrained minimizer. This analysis highlights important trade-offs between risk minimization and achieving fairnes. The theoretical solutions are also used as the basis for construction of flexible semiparametric estimation strategies for these nuisance components. We describe the robustness properties of our estimators in terms of achieving the optimal constrained risk, as well as in terms of controlling the value of the constraint. We study via simulation the impact of using robust estimators of pathway-specific effects to validate our theory. This work advances the discourse on algorithmic fairness by integrating complex causal considerations into model training, thus providing strategies for implementing fair models in real-world applications.

翻译：本文提出了一种利用机器学习估计公平最优预测的框架，其中公平性概念可通过路径特定因果效应进行量化。我们采用一种基于拉格朗日乘子的无限维函数估计方法，推导出基于均方误差和交叉熵风险准则的约束优化闭式解。对这些解的理论形式进行了详细分析，并将其描述为对无约束最小化器的精细调整。该分析揭示了风险最小化与实现公平性之间的重要权衡。理论解还作为构建这些干扰成分的灵活半参数估计策略的基础。我们从实现最优约束风险和控制约束值两个角度描述了估计量的稳健性。通过模拟研究使用路径特定效应的稳健估计量所产生的影响，以验证我们的理论。这项工作通过将复杂的因果考量整合到模型训练中，推进了算法公平性的讨论，从而为实际应用中实施公平模型提供了策略。