We revisit the problem of online learning with individual fairness, where an online learner strives to maximize predictive accuracy while ensuring that similar individuals are treated similarly. We first extend the frameworks of Gillen et al. (2018); Bechavod et al. (2020), which rely on feedback from human auditors regarding fairness violations, as we consider auditing schemes that are capable of aggregating feedback from any number of auditors, using a rich class we term monotone aggregation functions. We then prove a characterization for such auditing schemes, practically reducing the analysis of auditing for individual fairness by multiple auditors to that of auditing by (instance-specific) single auditors. Using our generalized framework, we present an oracle-efficient algorithm achieving an upper bound frontier of $(\mathcal{O}(T^{1/2+2b}),\mathcal{O}(T^{3/4-b}))$ respectively for regret, number of fairness violations, for $0\leq b \leq 1/4$. We then study an online classification setting where label feedback is available for positively-predicted individuals only, and present an oracle-efficient algorithm achieving an upper bound frontier of $(\mathcal{O}(T^{2/3+2b}),\mathcal{O}(T^{5/6-b}))$ for regret, number of fairness violations, for $0\leq b \leq 1/6$. In both settings, our algorithms improve on the best known bounds for oracle-efficient algorithms. Furthermore, our algorithms offer significant improvements in computational efficiency, greatly reducing the number of required calls to an (offline) optimization oracle per round, to $\tilde{\mathcal{O}}(\alpha^{-2})$ in the full information setting, and $\tilde{\mathcal{O}}(\alpha^{-2} + k^2T^{1/3})$ in the partial information setting, where $\alpha$ is the sensitivity for reporting fairness violations, and $k$ is the number of individuals in a round.

翻译：我们重新审视在线学习中的个体公平性问题，即在线学习者在最大化预测准确率的同时确保相似个体获得相似对待。首先，我们扩展了Gillen等人（2018）和Bechavod等人（2020）的框架，这些框架依赖人类审计师对公平性违规行为的反馈。我们考虑能够聚合任意数量审计师反馈的审计机制，使用一类称为"单调聚合函数"的丰富函数类。随后，我们证明了此类审计机制的一个特征，实际上将多审计师个体公平性审计的分析简化为（实例特定的）单审计师审计。利用我们的广义框架，我们提出了一种面向oracle的高效算法，在$0\leq b \leq 1/4$条件下，分别获得了$(\mathcal{O}(T^{1/2+2b}),\mathcal{O}(T^{3/4-b}))$的遗憾值和公平性违规次数的上界前沿。接着，我们研究仅对正预测个体提供标签反馈的在线分类场景，并提出一种面向oracle的高效算法，在$0\leq b \leq 1/6$条件下，实现了$(\mathcal{O}(T^{2/3+2b}),\mathcal{O}(T^{5/6-b}))$的遗憾值和公平性违规次数上界前沿。在两种场景中，我们的算法均改进了已知的面向oracle高效算法的最优界。此外，我们的算法在计算效率上取得显著提升，大幅减少了每轮对（离线）优化oracle的调用次数：在完全信息场景中降至$\tilde{\mathcal{O}}(\alpha^{-2})$，在部分信息场景中降至$\tilde{\mathcal{O}}(\alpha^{-2} + k^2T^{1/3})$，其中$\alpha$为公平性违规报告灵敏度，$k$为每轮涉及的个体数量。