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Regression under demographic parity constraints via unlabeled post-processing
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Proposes a theory-driven, unlabeled, online post-processing method that enforces demographic parity in unaware regression via a discretized, entropy-regularized dual convex objective optimized with stochastic gradient methods that control gradient-mapping norms.
Problem
Regression under demographic parity when the sensitive attribute is unavailable at inference (unawareness), with a need for computationally efficient algorithms that have end-to-end theoretical guarantees.
Approach
Discretize the prediction support into a grid, add entropic regularization, and derive a smooth convex dual objective whose stochastic minimization (controlling the gradient-mapping norm rather than objective error) yields a fair randomized predictor using only unlabeled features; the method works online with i.i.d. streams.
Key results
- On Law School and Communities and Crime, the proposed DP-postproc is competitive with or outperforms ADW in both training regimes across unfairness thresholds.
- The theory gives fairness and risk both decaying at rate 1/sqrt(T) with beta = T/(8 log2 T) and L = sqrt(T).
- Iterating multiple times over the same unlabeled data gave a significant empirical improvement without new samples.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use DP-postproc instead of ADW | Regression under demographic parity constraints · Communities and Crime | risk and unfairness | Mixed |
| Use DP-postproc instead of ADW | Regression under demographic parity constraints · Law School | risk and unfairness | Mixed |
| Use the improved SGD version instead of SGD3 | DP-postproc · Law School and Communities and Crime | performance | Helped |
| Use accelerated SGD without restart instead of the restarted version | DP-postproc · Law School and Communities and Crime | performance | No clear effect |
Surprising findings
- Accelerated SGD without restarts performed nearly identically to the restarted version despite theory suggesting restarts.
- The SGD3 variant was outperformed by an improved accelerated version in the experiments.
Limitations
- Requires knowledge of the bound B on the regression function.
- Stationary-point guarantees for convex optimization may need further study to improve practical performance.
- Experiments are limited to two datasets with one binary sensitive attribute.
Experimental setup
Datasets: Law School Communities and Crime
Benchmarks: Law School Communities and Crime
Metrics: risk (MSE) unfairness
Baselines: ADW LinearRegression
Builds on: SGD3 discretization-based fair regression accelerated SGD with restarts
Closest papers by meaning
- Meta Optimality for Demographic Parity Constrained Regression via Post-Processing (ICML 2025 · similarity 0.91)
- Demographic Parity Constrained Minimax Optimal Regression under Linear Model (NeurIPS 2023 · similarity 0.89)
- Demographic parity in regression and classification within the unawareness framework (NeurIPS 2026 · similarity 0.88)
- Geometry of Relaxed Fair Regression: A Unified Framework for Aware and Unaware Settings (NeurIPS 2026 · similarity 0.86)
- Auditing and Enforcing Conditional Fairness via Optimal Transport (AAAI 2025 · similarity 0.85)
- Learning With Multi-Group Guarantees For Clusterable Subpopulations (ICML 2025 · similarity 0.83)
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