\emph{The Right to Explanation} and \emph{the Right to be Forgotten} are two important principles outlined to regulate algorithmic decision making and data usage in real-world applications. While the right to explanation allows individuals to request an actionable explanation for an algorithmic decision, the right to be forgotten grants them the right to ask for their data to be deleted from all the databases and models of an organization. Intuitively, enforcing the right to be forgotten may trigger model updates which in turn invalidate previously provided explanations, thus violating the right to explanation. In this work, we investigate the technical implications arising due to the interference between the two aforementioned regulatory principles, and propose \emph{the first algorithmic framework} to resolve the tension between them. To this end, we formulate a novel optimization problem to generate explanations that are robust to model updates due to the removal of training data instances by data deletion requests. We then derive an efficient approximation algorithm to handle the combinatorial complexity of this optimization problem. We theoretically demonstrate that our method generates explanations that are provably robust to worst-case data deletion requests with bounded costs in case of linear models and certain classes of non-linear models. Extensive experimentation with real-world datasets demonstrates the efficacy of the proposed framework.

翻译：《解释权》与《被遗忘权》是规范现实应用中算法决策与数据使用的两项重要原则。解释权允许个人就算法决策请求可操作的说明，而被遗忘权则赋予其要求组织从所有数据库和模型中删除个人数据的权利。直观上，执行被遗忘权可能触发模型更新，进而使先前提供的解释失效，从而违反了解释权。本研究探讨了上述两项监管原则间相互干扰所引发的技术影响，并提出了**首个算法框架**来化解二者之间的张力。为此，我们构建了一个新型优化问题，旨在生成对因数据删除请求导致训练样本移除而引发的模型更新具有鲁棒性的解释。继而，我们推导出一种高效近似算法以处理该优化问题的组合复杂性。我们理论上证明了：在线性模型及特定类别的非线性模型中，该方法生成的解释在面对最坏情况的数据删除请求时，具有以有界成本为代价的可证明鲁棒性。基于真实数据集的广泛实验验证了所提框架的有效性。