# Perfect Counterfactuals in Imperfect Worlds: Modelling Noisy Implementation of Actions in Sequential Algorithmic Recourse

arXiv: https://arxiv.org/abs/2410.02273 · HTML: https://mlsanity.com/paper/2410.02273/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 48 references that are in the map.
- First posted on arXiv 3 Oct 2024.

## Builds on (most cited first, 30 of 33)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [High-Dimensional Continuous Control Using Generalized Advantage Estimation](https://mlsanity.com/paper/1506.02438/) (2015)
- [OpenAI Gym](https://mlsanity.com/paper/1606.01540/) (2016)
- [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)
- [Actionable Recourse in Linear Classification](https://mlsanity.com/paper/1809.06514/) (2018)
- [FACE: Feasible and Actionable Counterfactual Explanations](https://mlsanity.com/paper/1909.09369/) (2019)
- [Interpretable Counterfactual Explanations Guided by Prototypes](https://mlsanity.com/paper/1907.02584/) (2019)
- [Model-Agnostic Counterfactual Explanations for Consequential Decisions](https://mlsanity.com/paper/1905.11190/) (2019)
- [Counterfactual Explanations and Algorithmic Recourses for Machine Learning: A Review](https://mlsanity.com/paper/2010.10596/) (2020)
- [Multi-Objective Counterfactual Explanations](https://mlsanity.com/paper/2004.11165/) (2020)
- [Learning Model-Agnostic Counterfactual Explanations for Tabular Data](https://mlsanity.com/paper/1910.09398/) (2019)
- [Towards Realistic Individual Recourse and Actionable Explanations in Black-Box Decision Making Systems](https://mlsanity.com/paper/1907.09615/) (2019)
- [The Hidden Assumptions Behind Counterfactual Explanations and Principal Reasons](https://mlsanity.com/paper/1912.04930/) (2019)
- [Counterfactual Explanations Can Be Manipulated](https://mlsanity.com/paper/2106.02666/) (2021)
- [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)
- [On Counterfactual Explanations under Predictive Multiplicity](https://mlsanity.com/paper/2006.13132/) (2020)
- [On the Adversarial Robustness of Causal Algorithmic Recourse](https://mlsanity.com/paper/2112.11313/) (2021)
- [Probabilistically Robust Recourse: Navigating the Trade-offs between Costs and Robustness in Algorithmic Recourse](https://mlsanity.com/paper/2203.06768/) (2022)
- [Counterfactual Explanations in Sequential Decision Making Under Uncertainty](https://mlsanity.com/paper/2107.02776/) (2021)
- [Algorithmic Recourse in the Wild: Understanding the Impact of Data and Model Shifts](https://mlsanity.com/paper/2012.11788/) (2020)
- [On the Robustness of Sparse Counterfactual Explanations to Adverse Perturbations](https://mlsanity.com/paper/2201.09051/) (2022)
- [Amortized Generation of Sequential Algorithmic Recourses for Black-box Models](https://mlsanity.com/paper/2106.03962/) (2021)
- [Synthesizing Action Sequences for Modifying Model Decisions](https://mlsanity.com/paper/1910.00057/) (2019)
- [Manipulation-Proof Machine Learning](https://mlsanity.com/paper/2004.03865/) (2020)
- [Generating robust counterfactual explanations](https://mlsanity.com/paper/2304.12943/) (2023)
- [Finding Counterfactually Optimal Action Sequences in Continuous State Spaces](https://mlsanity.com/paper/2306.03929/) (2023)
- [Probabilistically Plausible Counterfactual Explanations with Normalizing Flows](https://mlsanity.com/paper/2405.17640/) (2024)

## Built on by (most cited first, 2 of 2)

- [Reinforcement Learning for Durable Algorithmic Recourse](https://mlsanity.com/paper/2509.22102/) (2025)
- [Uncertainty Quantification as a Principled Foundation for Explainable Artificial Intelligence: A Case Study of Counterfactual Explanations](https://mlsanity.com/paper/2502.17007/) (2025)

## Abstract (arXiv)

Algorithmic recourse suggests actions to individuals who have been adversely affected by automated decision-making, helping them to achieve the desired outcome. Knowing the recourse, however, does not guarantee that users can implement it perfectly, either due to environmental variability or personal choices. Recourse generation should thus anticipate its sub-optimal or noisy implementation. While several approaches construct recourse that is robust to small perturbations -- e.g., arising due to its noisy implementation -- they assume that the entire recourse is implemented in a single step, thus model the noise as one-off and uniform. But these assumptions are unrealistic since recourse often entails multiple sequential steps, which makes it harder to implement and subject to increasing noise. In this work, we consider recourse under plausible noise that adheres to the local data geometry and accumulates at every step of the way. We frame this problem as a Markov Decision Process and demonstrate that such a distribution of plausible noise satisfies the Markov property. We then propose the RObust SEquential (ROSE) recourse generator for tabular data; our method produces a series of steps leading to the desired outcome even when they are implemented imperfectly. Given plausible modelling of sub-optimal human actions and greater recourse robustness to accumulated uncertainty, ROSE provides users with a high chance of success while maintaining low recourse cost. Empirical evaluation shows that our algorithm effectively navigates the inherent trade-off between recourse robustness and cost while ensuring its sparsity and computational efficiency.