_NeurIPS_Camera_Ready__Actionable_Recourse_for_Subgroups (4)

In order to prove that the objective function in Eqn. 1 is non-normal, non-negative, non-monotone, and submodular, we need to prove the following: any one of the terms in the objective is non-normal all the terms in the objective are non-negative any one of the terms in the objective is non-monotone all the terms in the objective are submodular Non-normality Let us consider the term f This metric can never be negative by definition. This is clearly a diminishing returns function i.e., more additional instances in the data are covered Before we prove Theorem 2.2, we will first discuss how several previously proposed methods which Eqn.1 can be reduced to the objectives employed by prior approaches which provide instance level Subsuming other objective functions: The objective optimized by Wachter et al. is Higher values of recourse accuracy are desired; lower values of mean fcost are desired. Explanation vs. Recourse Accuracy for COMP AS (left), Credit (middle), and Bail (right) datasets A.2.2 User Study We manually constructed a two level recourse set (as our black box model) for the bail application. We deliberately ensured that this black box was biased against individuals who are not Caucasian. This two level recourse set (black box) is shown in Figure 4. We used AR-LIME as a comparison point in our user study.