Research map / Learning theory and algorithms / Fairness
Audits Under Resource, Data, and Access Constraints: Scaling Laws For Less Discriminatory Alternatives
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Gives a closed-form upper bound on the BCE-vs-demographic-parity Pareto frontier that acts as a scaling law, letting claimants fit the frontier with small models and extrapolate to contested large models for less-discriminatory-alternative (LDA) claims.
Problem
Under the less discriminatory alternative (LDA) requirement in US anti-discrimination law, claimants bear the burden of proving a less discriminatory model exists, but they lack compute, data, and access to the contested model, creating a resource-information asymmetry.
Approach
Recast LDA existence as determining the loss-fairness Pareto frontier, derive a closed-form upper bound on that frontier under a stylized data-generating process by using an artificial tilted training distribution and a model-symmetry assumption, and use it as a scaling law: fit its constants on small models and extrapolate to large model size and data.
Key results
- Fitted scaling law for the loss-fairness Pareto frontier matches empirical frontiers on synthetic data, with fitted loss scaling 55(N^-0.7 + D^-0.5).
- Closed-form bound applies even when the data-generating process violates independence of X and A (A depends on X in experiments).
- Claimed that as few as 7 small models suffice to fit the seven constants of the scaling law.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use the closed-form scaling law fitted on smaller models to predict larger-model Pareto frontiers | Loss-fairness scaling law · Synthetic data | Pareto frontier fit | Helped |
| Relax the assumption that features and group labels are independent | Loss-fairness scaling law · Synthetic data with X not independent of A | Pareto frontier fit | No clear effect |
Surprising findings
- The theory predicts the effect of scaling on the bound is linearly additive, and experiments support this.
- Fitting multiple parameter sets can match the same empirical frontier, so the fit is non-unique.
Limitations
- Theory holds only for a stylized data-generating process, a model-symmetry assumption on Pareto-optimal models, and an inequality (upper bound).
- Experiments are limited to synthetic data with small models; no real datasets or large-scale runs.
- Restricted to BCE loss and demographic parity; other metrics left to future work.
Experimental setup
Datasets: synthetic data (10,000 samples, 20-dimensional Gaussian features)
Benchmarks: synthetic data
Metrics: binary cross-entropy loss demographic parity gap
Builds on: neural scaling laws (Kaplan et al.) Chinchilla scaling law linear scalarization
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