The Statistical Fairness-Accuracy Frontier

Machine learning models must balance accuracy and fairness, but these goals often conflict, particularly when data come from multiple demographic groups. A useful tool for understanding this trade-off is the fairness-accuracy (FA) frontier, which characterizes the set of models that cannot be simultaneously improved in both fairness and accuracy. Prior analyses of the FA frontier provide a full characterization under the assumption of complete knowledge of population distributions -- an unrealistic ideal. We study the FA frontier in the finite-sample regime, showing how it deviates from its population counterpart and quantifying the worst-case gap between them. In particular, we derive minimax-optimal estimators that depend on the designer's knowledge of the covariate distribution. For each estimator, we characterize how finite-sample effects asymmetrically impact each group's risk, and identify optimal sample allocation strategies. Our results transform the FA frontier from a theoretical construct into a practical tool for policymakers and practitioners who must often design algorithms with limited data.

Fair Allocation in Dynamic Mechanism Design

We consider a dynamic mechanism design problem where an auctioneer sells an indivisible good to two groups of buyers in every round, for a total of $T$ rounds. The auctioneer aims to maximize their discounted overall revenue while adhering to a fairness constraint that guarantees a minimum average allocation for each group. We begin by studying the static case ($T=1$) and establish that the optimal mechanism involves two types of subsidization: one that increases the overall probability of allocation to all buyers, and another that favors the group which otherwise has a lower probability of winning the item. We then extend our results to the dynamic case by characterizing a set of recursive functions that determine the optimal allocation and payments in each round. Notably, our results establish that in the dynamic case, the seller, on the one hand, commits to a participation reward to incentivize truth-telling, and on the other hand, charges an entry fee for every round. Moreover, the optimal allocation once more involves subsidization in favor of one group, where the extent of subsidization depends on the difference in future utilities for both the seller and buyers when allocating the item to one group versus the other. Finally, we present an approximation scheme to solve the recursive equations and determine an approximately optimal and fair allocation efficiently.