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As machine learning models are increasingly being employed to makeconsequential decisions in real-world settings, it becomes critical to ensurethat individuals who are adversely impacted (e.g., loan denied) by thepredictions of these models are provided with a means for recourse. Whileseveral approaches have been proposed to construct recourses for affectedindividuals, 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 inherenttrade-offs between the recourse costs and robustness. Furthermore, priorapproaches do not provide end users with any agency over navigating theaforementioned trade-offs. In this work, we address the above challenges byproposing the first algorithmic framework which enables users to effectivelymanage the recourse cost vs. robustness trade-offs. More specifically, ourframework Probabilistically ROBust rEcourse (\texttt{PROBE}) lets users choosethe probability with which a recourse could get invalidated (recourseinvalidation rate) if small changes are made to the recourse i.e., the recourseis implemented somewhat noisily. To this end, we propose a novel objectivefunction 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 modelprediction. We develop novel theoretical results to characterize the recourseinvalidation rates corresponding to any given instance w.r.t. different classesof underlying models (e.g., linear models, tree based models etc.), andleverage these results to efficiently optimize the proposed objective.Experimental evaluation with multiple real world datasets demonstrates theefficacy of the proposed framework.

Probabilistically Robust Recourse: Navigating the Trade-offs between Costs and Robustness in Algorithmic Recourse