Optimal Robust Recourse with $L^p$-Bounded Model Change

2025-09-25

AI Summary

This work addresses the fragility of counterfactual recommendations in algorithmic decision systems under model updates. We propose a robust counterfactual explanation framework that generates minimum-cost, actionable recourse for adversely predicted individuals—guaranteed to remain valid under model perturbations bounded by an $L^p$ norm ($1 leq p < infty$). We derive, for the first time, a closed-form characterization of the optimal robust solution for generalized linear models under $L^p$ constraints and design an efficient non-convex optimization algorithm with theoretical guarantees on feasibility and robustness. Compared to standard $L^infty$-based approaches, our method reduces recourse cost by several orders of magnitude, while improving sparsity and the cost-effectiveness trade-off. Extensive experiments demonstrate superior performance across diverse models—including nonlinear ones—and strong robustness to post-hoc feasibility-preserving strategies.

Technology Category

• Machine Learning: Adversarial Learning & Robustness
• Search and Optimization: Adversarial Search
• Computer Vision: Adversarial Attacks & Robustness

Application Category

• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

Recourse provides individuals who received undesirable labels (e.g., denied a loan) from algorithmic decision-making systems with a minimum-cost improvement suggestion to achieve the desired outcome. However, in practice, models often get updated to reflect changes in the data distribution or environment, invalidating the recourse recommendations (i.e., following the recourse will not lead to the desirable outcome). The robust recourse literature addresses this issue by providing a framework for computing recourses whose validity is resilient to slight changes in the model. However, since the optimization problem of computing robust recourse is non-convex (even for linear models), most of the current approaches do not have any theoretical guarantee on the optimality of the recourse. Recent work by Kayastha et. al. provides the first provably optimal algorithm for robust recourse with respect to generalized linear models when the model changes are measured using the $L^{infty}$ norm. However, using the $L^{infty}$ norm can lead to recourse solutions with a high price. To address this shortcoming, we consider more constrained model changes defined by the $L^p$ norm, where $pgeq 1$ but $p eq infty$, and provide a new algorithm that provably computes the optimal robust recourse for generalized linear models. Empirically, for both linear and non-linear models, we demonstrate that our algorithm achieves a significantly lower price of recourse (up to several orders of magnitude) compared to prior work and also exhibits a better trade-off between the implementation cost of recourse and its validity. Our empirical analysis also illustrates that our approach provides more sparse recourses compared to prior work and remains resilient to post-processing approaches that guarantee feasibility.

Problem

• Computing optimal recourse resilient to model changes under L^p norms
• Addressing high cost limitations of existing L^∞ robust recourse methods
• Providing provably optimal recourse for generalized linear models

Innovation

• Optimal robust recourse for Lp-bounded model changes
• Provably optimal algorithm for generalized linear models
• Lower cost recourses with better validity trade-offs