Source-linked AI summary
A survey of algorithmic recourse: definitions, formulations, solutions, and prospects
Amir-Hossein Karimi, Gilles Barthe, Bernhard Schölkopf, Isabel Valera
TL;DR
Automated decisions in consequential settings create a need for recourse that helps adversely affected individuals understand and change outcomes. This survey unifies recourse definitions, formulations, and solutions, distinguishes contrastive explanations from causal recommendations, and identifies unresolved assumptions and evaluation gaps. It concludes that realistic recourse involves diverse constraints and trade-offs with fairness, security, privacy, and robustness.
Problem
Individuals adversely treated by automated decisions need explanations and recommendations to improve outcomes in consequential settings.
Method
The paper performs a literature review that unifies recourse definitions, formulations, technical solutions, constraints, and connections to ethical machine learning.
Results
The survey distinguishes contrastive explanations from consequential recommendations and summarizes their different technical treatments across diverse recourse setups.
Takeaways & Limitations
Realistic recourse requires attention to individual- and context-dependent constraints and trade-offs among fairness, security, privacy, and robustness.
Takeaways & Limitations
Deterministic consequential recourse depends on strong causal assumptions, including knowledge of the true structural causal model or a causally sufficient graph.
Abstract
from arXiv · showhide
Machine learning is increasingly used to inform decision-making in sensitive situations where decisions have consequential effects on individuals' lives. In these settings, in addition to requiring models to be accurate and robust, socially relevant values such as fairness, privacy, accountability, and explainability play an important role for the adoption and impact of said technologies. In this work, we focus on algorithmic recourse, which is concerned with providing explanations and recommendations to individuals who are unfavourably treated by automated decision-making systems. We first perform an extensive literature review, and align the efforts of many authors by presenting unified definitions, formulations, and solutions to recourse. Then, we provide an overview of the prospective research directions towards which the community may engage, challenging existing assumptions and making explicit connections to other ethical challenges such as security, privacy, and fairness.
1 INTRODUCTION
Algorithmic recourse addresses how people adversely affected by automated decisions can understand and change their situations. The survey consolidates recourse research while situating it among broader ethical and legal concerns.
- Algorithmic recourse helps individuals obtain explanations and recommendations for favourably changing outcomes in consequential automated decisions.Such settings include finance, justice, healthcare, and hiring, where individuals may need to expend effort to change their situations.
- The review brings together recent work to consolidate definitions, establish technical baselines, and connect recourse with broader ethical machine learning literature.
- It provides a unified overview of definitions, formulations, and technical solutions for contrastive explanations and consequential recommendations.The survey covers a broad range of setups and distinguishes the different technical treatment of these two recourse offerings.
- The document targets practitioners, researchers, and legal scholars through technical overviews, a survey of 50+ papers, and discussion of ethical machine learning connections.
- The survey briefly introduces related topics rather than comprehensively reviewing explainable machine learning, causal inference, counterfactual inference, or optimization.
2 BACKGROUND
The paper distinguishes contrastive explanations from consequential recommendations by whether interventions alter model inputs independently or act through causal relationships. It surveys formulations and methods while emphasizing that realistic recourse remains difficult to compare and support broadly.
- 2.1 Recourse definitions: Recourse requires an affected individual to understand and act to alleviate an unfavourable situation, thereby exercising temporally extended agency.
- 2.2 Recourse and causality: Contrastive explanations independently shift black-box inputs, whereas consequential recommendations intervene on a causal model and may produce downstream effects.Consequential recommendations require accurate knowledge of the structural causal model or causal graph.
- 2.2 Recourse and causality: Contrastive explanations ask what profile would have produced a favourable outcome, while consequential recommendations ask what actions would have produced that profile.
- 2.2.3 Clarifying terminology: contrastive, consequential,: The literature mostly targets contrastive explanations, supports differentiable models widely, and sparsely supports many constraints while trading off optimality, coverage, runtime, and access.The survey cautions that its table is not a ranking or qualitative comparison because methods use different setups.
3 FORMULATION
The paper formulates recourse as two related optimization problems: finding nearby contrastive explanations or finding feasible, low-cost actions that causally produce favorable outcomes. It emphasizes that distances, costs, constraints, and data types must reflect real-world structure rather than technical convenience alone.
- 3 FORMULATION: Contrastive explanations search for plausible instances with a different prediction, while consequential recommendations search for feasible actions whose structural counterfactual changes the outcome.The two formulations differ because feature perturbations need not correspond directly to actions an individual can perform.
- 3 FORMULATION: Solving the contrastive formulation yields a nearest counterfactual explanation but no direct recommendation, whereas solving the consequential formulation yields both an action and its induced explanation.The induced counterfactual is generated through the structural causal model rather than independent feature shifts.
- 3 FORMULATION: The authors prioritize minimal consequential recommendations that produce a favorable explanation, although extra assumptions often lead existing work to solve the contrastive problem instead.They note that nearest explanations may be unattainable through minimal effort.
- 3.1 Optimization objective: Distances and action costs are difficult to define because effort can be asymmetric and salient reasons lack formal legal guidance.The paper argues that these definitions require interdisciplinary engagement and cannot arise from technical considerations alone.
- 3.1 Optimization objective: Reviewed distance measures include MAD-weighted Manhattan distance and weighted combinations of ℓ0, ℓ1, ℓ2, and ℓ∞ norms for balancing sparsity, elastic distance, and maximum feature change.Other approaches measure dissimilarity on graph manifolds or learned and Riemannian latent spaces.
- 3.1 Optimization objective: Action costs can use norms, constant action costs, user-specified cost matrices, or percentile shifts that account for the difficulty of reaching unlikely regions of the data distribution.A move from the 50th to 55th percentile is presented as easier than a move from the 90th to 95th percentile.
- 3.1 Optimization objective: When changing one variable leaves others unaffected, distance and cost can mirror one another, but the paper rejects a general one-to-one mapping between them.Causal dependencies can make an action on one variable produce changes in other model inputs.
- 3.5 Datatypes and encoding: Categorical encodings require mutually exclusive categories, thermometer encodings require ordered inequalities, and related formulations distinguish recourse from profit-oriented actionable knowledge extraction.The review covers these datatype constraints while contrasting recourse’s trust-oriented use with business-objective optimization.
4 SOLUTION
The paper reviews recourse solvers across differentiable, nondifferentiable, linear, heuristic, and model-access settings. It evaluates them against competing goals such as optimality, coverage, runtime, and access, which practical methods often cannot satisfy simultaneously.
- 4 SOLUTION: Recourse objectives and classifier constraints may be nonlinear, non-convex, or non-differentiable, making general optimization difficult.The minimized distance or cost and the model constraint need not have simple mathematical structure.
- 4 SOLUTION: Methods commonly trade off optimal guarantees, perfect coverage, and efficient runtime, while sometimes requiring prohibitive access to data or the predictive model.These competing desiderata define practical limits on solver selection.
- 4 SOLUTION: Optimality seeks at least one proximal solution, while coverage measures how many individuals receive a plausible counterfactual when a solution exists.Communicating applicability is important for building trust.
- 4 SOLUTION: Near-real-time generation is desirable because recourse may be delivered conversationally, favoring efficient and interactive algorithms.Runtime is therefore treated as a practical solver criterion rather than merely a computational convenience.
- 4 SOLUTION: Model access ranges from label-only queries through gradients and class probabilities to complete white-box parameter access.Different optimization approaches require different points on this access spectrum.
- 4 SOLUTION: Organizations may avoid sharing training data, model parameters, or unrestricted model APIs with third parties, restricting feasible recourse tools.This makes deployment setting and ownership relevant to solver choice.
- 4 SOLUTION: Differentiable methods use gradient optimization, whereas nondifferentiable problems may use branch-and-bound; linear discrete or mixed problems can use ILP or MILP solvers.The choice depends on objective, constraint, and datatype structure.
- 4 SOLUTION: Heuristic approaches include graph shortest paths and genetic search, with genetic methods offering model-, datatype-, and norm-agnostic operation using only query access.These methods trade formal optimization structure for broader applicability.
5 PROSPECTS
The survey identifies open problems that extend recourse beyond fixed, individual, deterministic settings and connect it to security, fairness, robustness, and benchmarking.
- Existing recourse setups assume known, stationary world dynamics, fixed predictive models, individual-only changes, truthful agents, and aligned objectives.
- 5.1 Beyond deterministic recourse: Exact consequential recourse requires the true structural causal model, while incomplete causal knowledge makes deterministic recourse impossible and introduces uncertainty.High-probability methods still assume a causally sufficient graph; hidden confounders and partially observed graphs remain open settings.
- 5.3 Beyond individualized recourse: Recourse should extend beyond single individuals to representatives, fiduciaries, groups, and sub-populations with adjusted action costs and feasibility constraints.Collective action can make individually costly or non-actionable background variables actionable at group level, but modeling such considerations remains open.
- 5.4 On the interplay of recourse and ethical ML: Fairness of recourse is distinct from fairness of prediction: demographically fair predictions can still require larger average recourse actions for one subgroup.Equalizing Recourse calibrates average distance to the decision boundary across subgroups, while action-cost equalization is proposed as a natural extension.
- 5.4 On the interplay of recourse and ethical ML: Recourse explanations may expose private information and system vulnerabilities, enabling model extraction and creating tensions between diverse offerings and security.Regulatory oversight, random audits, or minimum numbers of diverse recourse offerings are discussed, with the latter potentially conflicting with security.
- 5.5 Towards unifying benchmarks: A comparative benchmark is lacking, motivating an online challenge with multiple tracks to evaluate existing and new recourse methods objectively.The need is especially acute for consequential recommendations, which depend on assumptions about the causal generative process.
6 CONCLUSIONS
The survey distinguishes contrastive explanations from consequential recommendations and emphasizes minimal recommendations because they directly optimize for individual effort. It unifies realistic recourse constraints while identifying open directions involving trade-offs among fairness, security, privacy, and robustness.
- Consequential recommendations are under-explored because they require additional assumptions about the world's causal generative process.
- Minimal consequential recommendations prioritize the least effort from the individual, unlike nearest contrastive explanations.
- Realistic recourse formulations require context-dependent constraints such as actionability, plausibility, diversity, and sparsity.
- The survey distinguishes distance from cost and plausibility from actionability or feasibility, distinctions often ignored in prior work.
- Future recourse research must address tensions among fairness, security, privacy, and robustness, potentially requiring new definitions and techniques.