Algorithmic Fairness is an established area of machine learning, willing to reduce the influence of hidden bias in the data. Yet, despite its wide range of applications, very few works consider the multi-class classification setting from the fairness perspective. We focus on this question and extend the definition of approximate fairness in the case of Demographic Parity to multi-class classification. We specify the corresponding expressions of the optimal fair classifiers. This suggests a plug-in data-driven procedure, for which we establish theoretical guarantees. The enhanced estimator is proved to mimic the behavior of the optimal rule both in terms of fairness and risk. Notably, fairness guarantees are distribution-free. The approach is evaluated on both synthetic and real datasets and reveals very effective in decision making with a preset level of unfairness. In addition, our method is competitive (if not better) with the state-of-the-art in binary and multi-class tasks.

翻译：算法公平是一个公认的机器学习领域,愿意减少数据中隐蔽偏见的影响。然而,尽管应用范围很广,但很少有工作从公平的角度考虑多级分类设置。我们注重这一问题,并将人口均等情况下的近似公平定义扩大到多级分类。我们具体规定了最佳公平分类者的相应表达方式。这表示了一个插头数据驱动程序,为此我们建立了理论保障。强化的估量器在公平性和风险方面都模仿了最佳规则的行为。值得注意的是,公平保障是无分配的。这种方法在合成和真实数据集上都进行了评估,并显示在决策中非常有效,而且预设了不公平的程度。此外,我们的方法与二元和多级任务中的最新技术相比具有竞争力(如果不是更好的话)。</s>