# Distributionally Robust Recourse Action

arXiv: https://arxiv.org/abs/2302.11211 · HTML: https://mlsanity.com/paper/2302.11211/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 59 references that are in the map.
- First posted on arXiv 22 Feb 2023.

## Builds on (most cited first, 27 of 27)

- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Can You Trust Your Model's Uncertainty? Evaluating Predictive Uncertainty Under Dataset Shift](https://mlsanity.com/paper/1906.02530/) (2019)
- [Counterfactual Explanations without Opening the Black Box: Automated Decisions and the GDPR](https://mlsanity.com/paper/1711.00399/) (2017)
- [Explaining Machine Learning Classifiers through Diverse Counterfactual Explanations](https://mlsanity.com/paper/1905.07697/) (2019)
- [Deep Ensembles: A Loss Landscape Perspective](https://mlsanity.com/paper/1912.02757/) (2019)
- [Fairness Without Demographics in Repeated Loss Minimization](https://mlsanity.com/paper/1806.08010/) (2018)
- [Actionable Recourse in Linear Classification](https://mlsanity.com/paper/1809.06514/) (2018)
- [Algorithmic Recourse: from Counterfactual Explanations to Interventions](https://mlsanity.com/paper/2002.06278/) (2020)
- [Model-Agnostic Counterfactual Explanations for Consequential Decisions](https://mlsanity.com/paper/1905.11190/) (2019)
- [Statistics of Robust Optimization: A Generalized Empirical Likelihood Approach](https://mlsanity.com/paper/1610.03425/) (2016)
- [Counterfactual Explanations and Algorithmic Recourses for Machine Learning: A Review](https://mlsanity.com/paper/2010.10596/) (2020)
- [Wasserstein Distributionally Robust Optimization: Theory and Applications in Machine Learning](https://mlsanity.com/paper/1908.08729/) (2019)
- [Multi-Objective Counterfactual Explanations](https://mlsanity.com/paper/2004.11165/) (2020)
- [Variance-based regularization with convex objectives](https://mlsanity.com/paper/1610.02581/) (2016)
- [Efficient Search for Diverse Coherent Explanations](https://mlsanity.com/paper/1901.04909/) (2019)
- [Towards Robust and Reliable Algorithmic Recourse](https://mlsanity.com/paper/2102.13620/) (2021)
- [CARLA: A Python Library to Benchmark Algorithmic Recourse and Counterfactual Explanation Algorithms](https://mlsanity.com/paper/2108.00783/) (2021)
- [Data-Driven Robust Optimization](https://mlsanity.com/paper/1401.0212/) (2013)
- [On Counterfactual Explanations under Predictive Multiplicity](https://mlsanity.com/paper/2006.13132/) (2020)
- [Consistent Counterfactuals for Deep Models](https://mlsanity.com/paper/2110.03109/) (2021)
- [Algorithmic Recourse in the Wild: Understanding the Impact of Data and Model Shifts](https://mlsanity.com/paper/2012.11788/) (2020)
- [On the computation of counterfactual explanations -- A survey](https://mlsanity.com/paper/1911.07749/) (2019)
- [Counterfactual Plans under Distributional Ambiguity](https://mlsanity.com/paper/2201.12487/) (2022)
- [Robust Bayesian Recourse](https://mlsanity.com/paper/2206.10833/) (2022)
- [Sequential Domain Adaptation by Synthesizing Distributionally Robust Experts](https://mlsanity.com/paper/2106.00322/) (2021)
- [Mean-Covariance Robust Risk Measurement](https://mlsanity.com/paper/2112.09959/) (2021)

## Built on by (most cited first, 12 of 12)

- [Robust Counterfactual Explanations in Machine Learning: A Survey](https://mlsanity.com/paper/2402.01928/) (2024)
- [Time Can Invalidate Algorithmic Recourse](https://mlsanity.com/paper/2410.08007/) (2024)
- [Feature Responsiveness Scores: Model-Agnostic Explanations for Recourse](https://mlsanity.com/paper/2410.22598/) (2024)
- [Performative Validity of Recourse Explanations](https://mlsanity.com/paper/2506.15366/) (2025)
- [Interval Abstractions for Robust Counterfactual Explanations](https://mlsanity.com/paper/2404.13736/) (2024)
- [Learning-Augmented Robust Algorithmic Recourse](https://mlsanity.com/paper/2410.01580/) (2024)
- [Optimal Robust Recourse with Lp-Bounded Model Change](https://mlsanity.com/paper/2509.21293/) (2025)
- [Reinforcement Learning for Durable Algorithmic Recourse](https://mlsanity.com/paper/2509.22102/) (2025)
- [Verified Training for Counterfactual Explanation Robustness under Data Shift](https://mlsanity.com/paper/2403.03773/) (2024)
- [The Role of Causality in Algorithmic Recourse](https://mlsanity.com/paper/2607.28497/) (2026)
- [Responsiveness Verification: Will Predictions Change? How Much? How Often?](https://mlsanity.com/paper/2507.02169/) (2025)
- [Algorithmic Recourse Under Competition](https://mlsanity.com/paper/2609.39877/) (2026)

## Abstract (arXiv)

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.