As machine learning models are increasingly being employed to make consequential decisions in real-world settings, it becomes critical to ensure that individuals who are adversely impacted (e.g., loan denied) by the predictions of these models are provided with a means for recourse. While several approaches have been proposed to construct recourses for affected individuals, the recourses output by these methods either achieve low costs (i.e., ease-of-implementation) or robustness to small perturbations (i.e., noisy implementations of recourses), but not both due to the inherent trade-offs between the recourse costs and robustness. Furthermore, prior approaches do not provide end users with any agency over navigating the aforementioned trade-offs. In this work, we address the above challenges by proposing the first algorithmic framework which enables users to effectively manage the recourse cost vs. robustness trade-offs. More specifically, our framework Probabilistically ROBust rEcourse (\texttt{PROBE}) lets users choose the probability with which a recourse could get invalidated (recourse invalidation rate) if small changes are made to the recourse i.e., the recourse is implemented somewhat noisily. To this end, we propose a novel objective function which simultaneously minimizes the gap between the achieved (resulting) and desired recourse invalidation rates, minimizes recourse costs, and also ensures that the resulting recourse achieves a positive model prediction. We develop novel theoretical results to characterize the recourse invalidation rates corresponding to any given instance w.r.t. different classes of underlying models (e.g., linear models, tree based models etc.), and leverage these results to efficiently optimize the proposed objective. Experimental evaluation with multiple real world datasets demonstrates the efficacy of the proposed framework.

翻译：随着机器学习模型越来越多地被用于现实世界中的关键决策（例如贷款拒绝），确保受到这些模型预测不利影响的个体能够获得补救手段变得至关重要。尽管已有多种方法可为受影响个体构建补救措施，但这些方法输出的补救方案要么成本较低（即易于实施），要么对小扰动具有鲁棒性（即噪声化实施），但由于补救成本与鲁棒性之间存在固有权衡，尚未有方案能同时兼顾两者。此外，现有方法并未赋予终端用户自主管理上述权衡的能力。针对这些挑战，本文提出首个算法框架，使用户能够有效管理补救成本与鲁棒性之间的权衡。具体而言，我们的框架——概率鲁棒性补救（PROBE）——允许用户选择在补救措施发生微小变化（即近似噪声化实施）时，该补救方案失效的概率（即补救失效概率）。为此，我们提出一种新型目标函数，可同时最小化实际（实现）补救失效概率与目标失效概率之间的差距、最小化补救成本，并确保最终补救方案能获得正向模型预测。我们针对不同底层模型类别（如线性模型、基于树的模型等）开发了新颖的理论结果，以刻画任意给定实例对应的补救失效概率，并利用这些结果高效优化所提目标函数。在多个真实数据集上的实验评估验证了所提框架的有效性。