# Amortized Generation of Sequential Algorithmic Recourses for Black-box Models

arXiv: https://arxiv.org/abs/2106.03962 · HTML: https://mlsanity.com/paper/2106.03962/

## Key facts

- Cited by 24 papers in the map (data through 14 Oct 2026).
- Builds on 42 of its 80 references that are in the map.
- First posted on arXiv 7 Jun 2021.

## Builds on (most cited first, 30 of 42)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Grad-CAM: Visual Explanations from Deep Networks via Gradient-based Localization](https://mlsanity.com/paper/1610.02391/) (2016)
- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [Learning Deep Features for Discriminative Localization](https://mlsanity.com/paper/1512.04150/) (2015)
- [Asynchronous Methods for Deep Reinforcement Learning](https://mlsanity.com/paper/1602.01783/) (2016)
- [High-Dimensional Continuous Control Using Generalized Advantage Estimation](https://mlsanity.com/paper/1506.02438/) (2015)
- [OpenAI Gym](https://mlsanity.com/paper/1606.01540/) (2016)
- [Explanation in Artificial Intelligence: Insights from the Social Sciences](https://mlsanity.com/paper/1706.07269/) (2017)
- [Counterfactual Explanations without Opening the Black Box: Automated Decisions and the GDPR](https://mlsanity.com/paper/1711.00399/) (2017)
- [A Survey Of Methods For Explaining Black Box Models](https://mlsanity.com/paper/1802.01933/) (2018)
- [Explaining Machine Learning Classifiers through Diverse Counterfactual Explanations](https://mlsanity.com/paper/1905.07697/) (2019)
- [A Survey on Explainable Artificial Intelligence (XAI): Towards Medical XAI](https://mlsanity.com/paper/1907.07374/) (2019)
- [Actionable Recourse in Linear Classification](https://mlsanity.com/paper/1809.06514/) (2018)
- [Explanations based on the Missing: Towards Contrastive Explanations with Pertinent Negatives](https://mlsanity.com/paper/1802.07623/) (2018)
- [Improving fairness in machine learning systems: What do industry practitioners need?](https://mlsanity.com/paper/1812.05239/) (2018)
- [Manipulating and Measuring Model Interpretability](https://mlsanity.com/paper/1802.07810/) (2018)
- [Algorithmic Recourse: from Counterfactual Explanations to Interventions](https://mlsanity.com/paper/2002.06278/) (2020)
- [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)
- [Local Rule-Based Explanations of Black Box Decision Systems](https://mlsanity.com/paper/1805.10820/) (2018)
- [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)
- [Preserving Causal Constraints in Counterfactual Explanations for Machine Learning Classifiers](https://mlsanity.com/paper/1912.03277/) (2019)
- [Algorithmic recourse under imperfect causal knowledge: a probabilistic approach](https://mlsanity.com/paper/2006.06831/) (2020)
- [Towards Realistic Individual Recourse and Actionable Explanations in Black-Box Decision Making Systems](https://mlsanity.com/paper/1907.09615/) (2019)
- [Expanding Explainability: Towards Social Transparency in AI systems](https://mlsanity.com/paper/2101.04719/) (2021)
- [A survey of algorithmic recourse: definitions, formulations, solutions, and prospects](https://mlsanity.com/paper/2010.04050/) (2020)
- [Efficient Search for Diverse Coherent Explanations](https://mlsanity.com/paper/1901.04909/) (2019)
- [Good Counterfactuals and Where to Find Them: A Case-Based Technique for Generating Counterfactuals for Explainable AI (XAI)](https://mlsanity.com/paper/2005.13997/) (2020)

## Built on by (most cited first, 24 of 24)

- [Stochastic Amortization: A Unified Approach to Accelerate Feature and Data Attribution](https://mlsanity.com/paper/2401.15866/) (2024)
- [Provably Robust and Plausible Counterfactual Explanations for Neural Networks via Robust Optimisation](https://mlsanity.com/paper/2309.12545/) (2023)
- [CounterNet: End-to-End Training of Prediction Aware Counterfactual Explanations](https://mlsanity.com/paper/2109.07557/) (2021)
- [Efficient XAI Techniques: A Taxonomic Survey](https://mlsanity.com/paper/2302.03225/) (2023)
- [Feature-based Learning for Diverse and Privacy-Preserving Counterfactual Explanations](https://mlsanity.com/paper/2209.13446/) (2022)
- [Personalized Algorithmic Recourse with Preference Elicitation](https://mlsanity.com/paper/2205.13743/) (2022)
- [TABCF: Counterfactual Explanations for Tabular Data Using a Transformer-Based VAE](https://mlsanity.com/paper/2410.10463/) (2024)
- [Performative Validity of Recourse Explanations](https://mlsanity.com/paper/2506.15366/) (2025)
- [Feasible Recourse Plan via Diverse Interpolation](https://mlsanity.com/paper/2302.11213/) (2023)
- [Navigating Explanatory Multiverse Through Counterfactual Path Geometry](https://mlsanity.com/paper/2306.02786/) (2023)
- [For Better or Worse: The Impact of Counterfactual Explanations' Directionality on User Behavior in xAI](https://mlsanity.com/paper/2306.07637/) (2023)
- [Prediction without Preclusion: Recourse Verification with Reachable Sets](https://mlsanity.com/paper/2308.12820/) (2023)
- [Perfect Counterfactuals in Imperfect Worlds: Modelling Noisy Implementation of Actions in Sequential Algorithmic Recourse](https://mlsanity.com/paper/2410.02273/) (2024)
- [Counterfactual Maps: What They Are and How to Find Them](https://mlsanity.com/paper/2602.09128/) (2026)
- [Principled Diverse Counterfactuals in Multilinear Models](https://mlsanity.com/paper/2201.06467/) (2022)
- [Iterative Partial Fulfillment of Counterfactual Explanations: Benefits and Risks](https://mlsanity.com/paper/2303.11111/) (2023)
- [Learning Actionable Counterfactual Explanations in Large State Spaces](https://mlsanity.com/paper/2404.17034/) (2024)
- [From Universal to Individualized Actionability: Revisiting Personalization in Algorithmic Recourse](https://mlsanity.com/paper/2604.08030/) (2026)
- [Learning impartial policies for sequential counterfactual explanations using Deep Reinforcement Learning](https://mlsanity.com/paper/2311.00523/) (2023)
- [Personalized Path Recourse for Reinforcement Learning Agents](https://mlsanity.com/paper/2312.08724/) (2023)
- [Cost-Adaptive Recourse Recommendation by Adaptive Preference Elicitation](https://mlsanity.com/paper/2402.15073/) (2024)
- [No Dtrain: Model-Agnostic Counterfactual Explanations Using Reinforcement Learning](https://mlsanity.com/paper/2405.18563/) (2024)
- [Agentic Search for Counterfactual Recourse under Fixed LLM Budgets](https://mlsanity.com/paper/2606.08696/) (2026)
- [Algorithmic Recourse Under Competition](https://mlsanity.com/paper/2609.39877/) (2026)

## Abstract (arXiv)

Explainable machine learning (ML) has gained traction in recent years due to the increasing adoption of ML-based systems in many sectors. Algorithmic Recourses (ARs) provide "what if" feedback of the form "if an input datapoint were x' instead of x, then an ML-based system's output would be y' instead of y." ARs are attractive due to their actionable feedback, amenability to existing legal frameworks, and fidelity to the underlying ML model. Yet, current AR approaches are single shot -- that is, they assume x can change to x' in a single time period. We propose a novel stochastic-control-based approach that generates sequential ARs, that is, ARs that allow x to move stochastically and sequentially across intermediate states to a final state x'. Our approach is model agnostic and black box. Furthermore, the calculation of ARs is amortized such that once trained, it applies to multiple datapoints without the need for re-optimization. In addition to these primary characteristics, our approach admits optional desiderata such as adherence to the data manifold, respect for causal relations, and sparsity -- identified by past research as desirable properties of ARs. We evaluate our approach using three real-world datasets and show successful generation of sequential ARs that respect other recourse desiderata.