Algorithmic Recourse

When an applicant is denied a loan, recourse provides the specific, actionable steps needed to reverse the decision. Instead of vague advice, the system generates a sparse counterfactual: 'Increase your credit score by 12 points and reduce your debt-to-income ratio by 5%.' This respects immutable features like age and ensures recommendations fall within the applicant's action set—only suggesting changes they can realistically make. Financial institutions use this to comply with regulations like the Equal Credit Opportunity Act, providing adverse action notices that are precise and individualized.

A model denies coverage for a specific treatment. Algorithmic recourse generates a contrastive explanation: 'Why was this treatment denied instead of the alternative?' It identifies the minimal clinical parameters that would flip the decision—such as a specific lab value threshold or a documented comorbidity. This enables physicians to understand the decision boundary and either adjust the treatment plan or provide missing documentation. The system enforces feasibility constraints by never suggesting changes to immutable biological markers, ensuring recommendations are clinically plausible.

A predictive model rejects an applicant. The recourse system provides a set of diverse counterfactuals: multiple distinct paths to acceptance. One path might suggest improving standardized test scores; another might recommend specific prerequisite coursework. This respects individual fairness by ensuring similar applicants receive similar recourse options. The system uses Mahalanobis distance to generate plausible counterfactuals that lie within the distribution of previously admitted students, avoiding unrealistic recommendations like 'be 5 years younger.'

An internal algorithm screens out a candidate for a promotion. Recourse explains exactly which actionable features—such as completing a specific certification or leading a cross-functional project—would change the outcome. The system enforces counterfactual fairness: the recommendation would be identical if the candidate's gender or ethnicity were different in a counterfactual world. This operationalizes individual fairness by comparing the candidate only to their counterfactual self, not to a protected group average. The action set is constrained to professional development activities within the employee's control.

A recidivism model assigns a high-risk classification, influencing parole decisions. Recourse provides a contrastive explanation identifying the minimal behavioral and programmatic changes that would lower the risk score. Recommendations might include completing a substance abuse program or maintaining verified employment for a specific duration. The system enforces recourse robustness—the recommendations remain valid even after model retraining—and respects causal constraints encoded in a structural causal model (SCM) to prevent suggesting changes that violate real-world causal order.

An applicant is quoted a high premium or denied coverage. The recourse engine generates a sparse counterfactual identifying the minimal set of modifiable risk factors: 'Install a monitored security system and complete a defensive driving course.' The system uses growing spheres algorithms to find the closest point on the other side of the decision boundary while respecting feasibility constraints—it never suggests changing age or medical history. Counterfactual proximity is measured using L1 distance to ensure the recommended changes are as minimal and achievable as possible.

A subset of algorithmic recourse that constrains recommended changes to only those features an individual can realistically control. It distinguishes between a mathematically minimal change and a practically feasible one.

• Key distinction: Not all counterfactuals are actionable
• Example: Recommending a user decrease their 'age' is mathematically valid but not actionable; suggesting they increase their 'credit history length' is
• Implementation: Requires a predefined action set specifying permissible feature modifications

The degree to which a counterfactual recommendation respects real-world constraints. Feasibility ensures the path to a favorable outcome is not blocked by immutable characteristics or causal dependencies.

• Causal feasibility: A recommendation to increase 'education level' must not contradict the fact that it causally depends on 'age'
• Temporal feasibility: Features that can only change in one direction over time (monotonicity) must be respected
• Contextual feasibility: Considers the user's environment, capabilities, and resource limitations

A formal specification of the permissible modifications a user can make to each feature. It defines the boundary between actionable and non-actionable changes and is the foundational input to any recourse algorithm.

• Structure: Can specify allowed ranges, monotonic directions (increase only), or discrete options
• Example: For a loan application, 'income' may be increased by up to 20%, 'credit inquiries' can only decrease, and 'zip code' is immutable
• Impact: A poorly defined action set leads to recourse that is mathematically valid but practically useless

A protected input attribute that cannot be changed and must be held constant when generating counterfactual explanations. Immutable features are the hard constraints of the recourse problem.

• Examples: Date of birth, place of birth, race, gender (in most regulatory contexts), and genetic markers
• Enforcement: Algorithms must use feasibility constraints to zero out gradients or mask perturbations on these dimensions
• Fairness nexus: Forcing changes to immutable features is a primary indicator of algorithmic discrimination

The property that a counterfactual recommendation remains valid and flips the prediction even after the underlying model is retrained or slightly updated. Non-robust recourse erodes user trust when recommendations expire.

• Problem: A counterfactual generated on model version M_t may not flip the prediction on M_{t+1}
• Causes: Model updates, data drift, and stochastic training procedures shift the decision boundary
• Solutions: Robust recourse algorithms explicitly model uncertainty in the decision boundary or generate counterfactuals that are deep within the target class region

A metric quantifying the distance between the original input instance and the generated counterfactual. It operationalizes the principle of minimal change and is a core objective in most generation algorithms.

• Common measures: L1 norm (encourages sparsity), L2 norm (penalizes large deviations), and Mahalanobis distance (accounts for feature correlations)
• Trade-off: Minimizing proximity often conflicts with maximizing plausibility and diversity
• Interpretation: Lower proximity means less effort required from the end-user to achieve recourse