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Wasserstein Distributionally Robust Optimization through the Lens of Structural Causal Models and Individual Fairness
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Formulates a causally fair Wasserstein DRO using a causally fair dissimilarity function built from an SCM, derives a strong duality theorem, explicit/first-order regularizers, and finite-sample guarantees with estimated SCMs, with experiments on Adult, COMPAS and a synthetic linear SCM.
Problem
Individual fairness in learning under distributional uncertainty when causal structure and sensitive attributes make standard metrics fail as DRO transport costs (the cost violates positive-definiteness).
Approach
Defines a causally fair dissimilarity function (CFDF) that is zero between an instance and its counterfactual twins and stable under minor non-sensitive shift interventions, proves a strong duality for DRO with this cost (taking sup over sensitive levels), and derives closed-form or first-order regularizers for linear and nonlinear SCMs.
Key results
- CDRO achieves lower Unfair Area Index than baselines for Delta = 0.05 and 0.01 across all scenarios (100 seeds), per the text's figures.
- CDRO shows slightly lower accuracy than ERM, which the authors describe as a common fairness–accuracy trade-off.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use CDRO instead of ERM | Logistic regression · Adult, COMPAS, and LIN | UAI (Δ = .05) | Helped |
| Use CDRO instead of ERM | Logistic regression · Adult, COMPAS, and LIN | UAI (Δ = 0.01) | Helped |
| Use CDRO instead of ERM | Logistic regression · Adult, COMPAS, and LIN | accuracy | Hurt |
Limitations
- Assumes additive noise models with known structural equations for the main results.
- Restricted to the additive-noise setting and linear SCMs for exact regularizers; general extensions omitted.
- Relationship to causal optimal transport left for future work.
Experimental setup
Datasets: Adult COMPAS LIN (synthetic linear SCM)
Benchmarks: Adult COMPAS
Metrics: accuracy Unfair Area Index
Baselines: ERM Adversarial Learning (AL) Ross method
Builds on: Wasserstein DRO strong duality adversarial learning counterfactual fairness
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