Cost-Adaptive Recourse Recommendation by Adaptive Preference Elicitation

TL;DR

The paper tackles the problem of personalized recourse under subject-specific costs by learning the cost function through adaptive preference elicitation and then generating cost-aware recourse using two methods that respect a confidence set of costs. The core idea is to model the subject cost as a Mahalanobis distance with an unknown matrix $A_0$, identify $A_0$ via adaptive pairwise questions (yielding a Chebyshev center $A_c^\star$ of the feasible set), and produce recourse that remains valid for all $A$ in the final set. It provides a gradient-based recourse applicable to white-box models and a graph-based sequential recourse for black-box settings, with robust optimization and generalizations to handle inconsistencies and multi-option questions. Empirical results on seven real-world datasets show cost reductions and strong validity compared to baselines, demonstrating practical benefits of cost-adaptive recourse in diverse scenarios.

Abstract

Algorithmic recourse recommends a cost-efficient action to a subject to reverse an unfavorable machine learning classification decision. Most existing methods in the literature generate recourse under the assumption of complete knowledge about the cost function. In real-world practice, subjects could have distinct preferences, leading to incomplete information about the underlying cost function of the subject. This paper proposes a two-step approach integrating preference learning into the recourse generation problem. In the first step, we design a question-answering framework to refine the confidence set of the Mahalanobis matrix cost of the subject sequentially. Then, we generate recourse by utilizing two methods: gradient-based and graph-based cost-adaptive recourse that ensures validity while considering the whole confidence set of the cost matrix. The numerical evaluation demonstrates the benefits of our approach over state-of-the-art baselines in delivering cost-efficient recourse recommendations.

Figures (7)

• Figure 1: Example of a gradient-based one-step recourse recommendation (left) and a graph-based sequential recourse recommendation (right) on the stroke prediction example. ✗ denotes the unfavorable outcomes, and ✓ denotes the favorable outcomes.
• Figure 2: Overall flow of our cost-adaptive recourse recommendation framework. The subject inputs an instance $x_0$. In each of $T$ rounds of question-answer, we first find the Chebyshev center of the set $\mathcal{U}_{\mathbb P}$, then select the next question that minimizes the distance to the Chebyshev center. We provide two methods to generate the cost-adaptive recourse: gradient-based and graph-based.
• Figure 3: Illustration of the Chebyshev center. Black lines represent the hyperplanes $\langle A, M_{ij} \rangle = \varepsilon$ for $(i, j) \in \mathbb P$ defining the boundaries of the polytope $\mathcal{U}_{\mathbb P}$. The ball centered at the Chebyshev center $A_c^\star$ with radius $r$ is the largest inscribed ball of $\mathcal{U}_{\mathbb P}$.
• Figure 4: The illustration of $\mathcal{G}$ shows negatively predicted samples as red circles and positively predicted samples as green circles. The input instance $x_0$ is a gray circle. The terminal edges and unreachable nodes of flows in $\mathcal{F}$ are blue edges and green nodes with white crosses, respectively.
• Figure 5: Impact of the number of questions $T$ to the average mean rank on synthetic data and three real-world datasets. As the number of questions increases, the mean rank tends to decrease, highlighting that the Chebyshev center tends closer to the ground truth $A_0$.

Theorems & Definitions (9)

• Theorem 3.1: Chebyshev center
• proof
• Proposition 4.1: Equivalent formulation
• proof : Proof of Proposition \ref{['prop:sp']}
• Theorem 5.1: Chebyshev center with inconsistent elicitation
• proof : Proof of Theorem \ref{['thm:chebyshev2']}
• Proposition C.1: Quadratic cost
• proof : Proof of Proposition \ref{['prop:LQR']}
• Remark C.2: Finite time horizon