Auditing Fairness by Betting

As algorithmic decision-making continues to increase in prevalence across both the private and public sectors [1, 2], there has been an increasing push to scrutinize the fairness of these systems. This has lead to an explosion of interest in so-called "algorithmic fairness", and a significant body of work has focused on both defining fairness and training models in fair ways (e.g., [3-5]). However, preventing and redressing harms in real systems also requires the ability to audit models in order to assess their impact; such algorithmic audits are an increasing area of focus for researchers and practitioners [6-9]. Auditing may begin during model development [10], but as model behavior often changes over time throughout real-world deployment in response to distribution shift or model updates [11, 12], it is often necessary to repeatedly audit the performance of algorithmic systems over time [8, 13]. Detecting whether deployed models continue to meet various fairness criteria is of paramount importance to deciding whether an automated decision-making system continues to act reliably and whether intervention is necessary. In this work, we consider the perspective of an auditor or auditing agency tasked with determining if a model deployed "in the wild" is fair or not. Data concerning the system's decisions are gathered over time (perhaps with the purpose of testing fairness but perhaps for another purpose) and our goal is to determine if there is sufficient evidence to conclude that the system is unfair. If a system is in fact unfair, we want to determine so as early as possible, both in order to avert harms to users and because auditing may require expensive investment to collect or label samples [8, 13]. Following the recent work of Taskesen et al. [14] and Si et al. [15], a natural statistical framework for thinking about this problem is hypothesis testing.