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Learning Fair Policies for Multi-Stage Selection Problems from Observational Data

AAAI 2024 · Learning theory and algorithms › Fairness · approach: Fair allocation and selection · 0 citations (OpenAlex)

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Proposes a multi-stage fair selection framework that learns interpretable linear selection policies from biased observational data using inverse probability weighting and sample average approximation, reformulated as a mixed binary conic program.

Problem

Learning fair multi-stage selection policies (e.g., hiring, loan approval, bail) from observational data where outcomes are only observed for selected candidates, so training data suffers selection bias and fairness constraints must hold on the future population.

Approach

Combine IPW-based counterfactual evaluation of selection policies with sample average approximation of an infinite chance-constrained program over linear stage-wise selection rules, using an epsilon-conservative approximation that yields a mixed binary conic (MIP) reformulation solvable by off-the-shelf solvers.

Key results

• On the synthetic data, the proposed IPW-based model reaches 76.51% precision and 0.031 unfairness versus 68.57% precision and 0.050 unfairness for the existing selection policy at N=800.
• Across semi-synthetic real datasets, the Fair model reduces unfairness by roughly 17% to 55% relative to the No-Fair model (e.g., 37.5% on German, 35.71% on COMPAS) with small precision loss.
• Without IPW (No-IPW), the learned policies violate selection constraints in up to 60% of test trials at N=2000, while IPW violations drop to 0% at larger sizes.

Measured effects reported in the paper

Surprising findings

• Without IPW, constraint violation ratios can remain high or even increase with training size (e.g., 60% at N=2000), showing naive fitting on selected data is unusable for future populations.

Limitations

• Experiments are restricted to two-stage selection and linear policies on small training sizes (N up to 3000).
• Real-world datasets are semi-synthetic because no multi-stage selection data exists; selection process is simulated.
• Solver time limit of 4 minutes means large-N solutions may not be optimal.

Experimental setup

Datasets: Adult German Credit COMPAS synthetic two-stage selection data

Benchmarks: Adult German Credit COMPAS synthetic two-stage selection data

Metrics: precision unfairness (equal opportunity disparity) constraint violation ratio training time

Baselines: No-IPW existing selection policy

Builds on: inverse probability weighting sample average approximation Rooney Rule analysis

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