Wasserstein Distributionally Robust Optimization Through the Lens of Structural Causal Models and Individual Fairness

Abstract: In recent years, Wasserstein Distributionally Robust Optimization (DRO) has garnered substantial interest for its efficacy in data-driven decision-making under distributional uncertainty. However, limited research has explored the application of DRO to address individual fairness concerns, particularly when considering causal structures and sensitive attributes in learning problems. To address this gap, we first formulate the DRO problem from causality and individual fairness perspectives. We then present the DRO dual formulation as an efficient tool to convert the DRO problem into a more tractable and computationally efficient form. Next, we characterize the closed form of the approximate worst-case loss quantity as a regularizer, eliminating the max-step in the min-max DRO problem. We further estimate the regularizer in more general cases and explore the relationship between DRO and classical robust optimization. Finally, by removing the assumption of a known structural causal model, we provide finite sample error bounds when designing DRO with empirical distributions and estimated causal structures to ensure efficiency and robust learning.