Audits Under Resource, Data, and Access Constraints: Scaling Laws For Less Discriminatory Alternatives

AI audits play a critical role in AI accountability and safety. One branch of the law for which AI audits are particularly salient is anti-discrimination law. Several areas of anti-discrimination law implicate the"less discriminatory alternative"(LDA) requirement, in which a protocol (e.g., model) is defensible if no less discriminatory protocol that achieves comparable performance can be found with a reasonable amount of effort. Notably, the burden of proving an LDA exists typically falls on the claimant (the party alleging discrimination). This creates a significant hurdle in AI cases, as the claimant would seemingly need to train a less discriminatory yet high-performing model, a task requiring resources and expertise beyond most litigants. Moreover, developers often shield information about and access to their model and training data as trade secrets, making it difficult to reproduce a similar model from scratch. In this work, we present a procedure enabling claimants to determine if an LDA exists, even when they have limited compute, data, information, and model access. We focus on the setting in which fairness is given by demographic parity and performance by binary cross-entropy loss. As our main result, we provide a novel closed-form upper bound for the loss-fairness Pareto frontier (PF). We show how the claimant can use it to fit a PF in the"low-resource regime,"then extrapolate the PF that applies to the (large) model being contested, all without training a single large model. The expression thus serves as a scaling law for loss-fairness PFs. To use this scaling law, the claimant would require a small subsample of the train/test data. Then, the claimant can fit the context-specific PF by training as few as 7 (small) models. We stress test our main result in simulations, finding that our scaling law holds even when the exact conditions of our theory do not.