DISTRIBUTIONALLY ROBUST RECOURSE ACTION

Abstract

A recourse action aims to explain a particular algorithmic decision by showing one specific way in which the instance could be modified to receive an alternate outcome. Existing recourse generation methods often assume that the machine learning model does not change over time. However, this assumption does not always hold in practice because of data distribution shifts, and in this case, the recourse action may become invalid. To redress this shortcoming, we propose the Distributionally Robust Recourse Action (DiRRAc) framework, which generates a recourse action that has a high probability of being valid under a mixture of model shifts. We formulate the robustified recourse setup as a min-max optimization problem, where the max problem is specified by Gelbrich distance over an ambiguity set around the distribution of model parameters. Then we suggest a projected gradient descent algorithm to find a robust recourse according to the min-max objective. We show that our DiRRAc framework can be extended to hedge against the misspecification of the mixture weights. Numerical experiments with both synthetic and three real-world datasets demonstrate the benefits of our proposed framework over state-of-the-art recourse methods.

1. INTRODUCTION

Post-hoc explanations of machine learning models are useful for understanding and making reliable predictions in consequential domains such as loan approvals, college admission, and healthcare. Recently, recourse has been rising as an attractive tool to diagnose why machine learning models have made a particular decision for a given instance. A recourse action provides a possible modification of the given instance to receive an alternate decision (Ustun et al., 2019). Consider, for example, the case of loan approvals in which a credit application is rejected. Recourse will offer the reasons for rejection by showing what the application package should have been to get approved. A concrete example of a recourse in this case may be "the monthly salary should be higher by $500" or "20% of the current debt should be reduced". A recourse action has a positive, forward-looking meaning: they list out a directive modification that a person should implement so that they can get a more favorable outcome in the future. If a machine learning system can provide the negative outcomes with the corresponding recourse action, it can improve user engagement and boost the interpretability at the same time (Ustun et al., 2019; Karimi et al., 2021b) . Explanations thus play a central role in the future development of human-computer interaction as well as human-centric machine learning. Despite its attractiveness, providing recourse for the negative instances is not a trivial task. For realworld implementation, designing a recourse needs to strike an intricate balance between conflicting criteria. First and foremost, a recourse action should be feasible: if the prescribed action is taken, then the prediction of a machine learning model should be flipped. Further, to avoid making a drastic change to the characteristics of the input instance, a framework for generating recourse should minimize the cost of implementing the recourse action. An algorithm for finding recourse must make changes to only features that are actionable and should leave immutable features (relatively) unchanged. For example, we must consider the date of birth as an immutable feature; in contrast, we can consider salary or debt amount as actionable features. Various solutions have been proposed to provide recourses for a model prediction (Karimi et al., 2021b; Stepin et al., 2021; Artelt & Hammer, 2019; Pawelczyk et al., 2021; 2020; Verma et al., 

