Fair classification and fair representation learning are two important problems in supervised and unsupervised fair machine learning, respectively. Fair classification asks for a classifier that maximizes accuracy on a given data distribution subject to fairness constraints. Fair representation maps a given data distribution over the original feature space to a distribution over a new representation space such that all classifiers over the representation satisfy fairness. In this paper, we examine the power of randomization in both these problems to minimize the loss of accuracy that results when we impose fairness constraints. Previous work on fair classification has characterized the optimal fair classifiers on a given data distribution that maximize accuracy subject to fairness constraints, e.g., Demographic Parity (DP), Equal Opportunity (EO), and Predictive Equality (PE). We refine these characterizations to demonstrate when the optimal randomized fair classifiers can surpass their deterministic counterparts in accuracy. We also show how the optimal randomized fair classifier that we characterize can be obtained as a solution to a convex optimization problem. Recent work has provided techniques to construct fair representations for a given data distribution such that any classifier over this representation satisfies DP. However, the classifiers on these fair representations either come with no or weak accuracy guarantees when compared to the optimal fair classifier on the original data distribution. Extending our ideas for randomized fair classification, we improve on these works, and construct DP-fair, EO-fair, and PE-fair representations that have provably optimal accuracy and suffer no accuracy loss compared to the optimal DP-fair, EO-fair, and PE-fair classifiers respectively on the original data distribution.

在监督和无监督公平机器学习中，公平分类和公平表示学习是两个重要问题。本文研究了在这两个问题中，随机化方法可以最小化由于公平约束引起的准确性损失，并提出了公平分类和公平表示的随机化解决方案，可以获得最优准确性且不引起准确性损失。

关于在公平分类和表示中的随机化的力量