As machine learning (ML) models are increasingly being deployed in high-stakes applications, policymakers have suggested tighter data protection regulations (e.g., GDPR, CCPA). One key principle is the "right to be forgotten" which gives users the right to have their data deleted. Another key principle is the right to an actionable explanation, also known as algorithmic recourse, allowing users to reverse unfavorable decisions. To date, it is unknown whether these two principles can be operationalized simultaneously. Therefore, we introduce and study the problem of recourse invalidation in the context of data deletion requests. More specifically, we theoretically and empirically analyze the behavior of popular state-of-the-art algorithms and demonstrate that the recourses generated by these algorithms are likely to be invalidated if a small number of data deletion requests (e.g., 1 or 2) warrant updates of the predictive model. For the setting of differentiable models, we suggest a framework to identify a minimal subset of critical training points which, when removed, maximize the fraction of invalidated recourses. Using our framework, we empirically show that the removal of as little as 2 data instances from the training set can invalidate up to 95 percent of all recourses output by popular state-of-the-art algorithms. Thus, our work raises fundamental questions about the compatibility of "the right to an actionable explanation" in the context of the "right to be forgotten", while also providing constructive insights on the determining factors of recourse robustness.

翻译：随着机器学习模型日益部署于高风险应用场景，政策制定者提出了更严格的数据保护法规（如GDPR、CCPA）。其中一项核心原则是"被遗忘权"，即用户有权要求删除其个人数据。另一项核心原则是可操作解释权（亦称算法追索权），允许用户逆转不利决策。迄今为止，尚不清楚这两项原则能否同时实现。为此，我们引入并研究了数据删除请求背景下的追索权失效问题。具体而言，我们通过理论与实证分析主流先进算法的行为，证明当少量数据删除请求（例如1至2条）触发预测模型更新时，这些算法生成的追索方案很可能失效。针对可微分模型场景，我们提出一个框架来识别关键训练点的最小子集：当这些数据被移除时，可使最大比例的追索方案失效。基于该框架的实证表明，仅从训练集中移除2个数据实例，即可使主流先进算法输出的追索方案中高达95%失效。因此，本研究不仅就"被遗忘权"语境下"可操作解释权"的兼容性提出根本性质疑，同时为追索方案的鲁棒性决定因素提供了建设性见解。