Wasserstein Distributionally Robust Optimization Through the Lens of Structural Causal Models and Individual Fairness
This work addresses fairness concerns in machine learning by integrating causal models into DRO, offering a method to enhance robustness and efficiency in data-driven decision-making, though it builds incrementally on existing DRO frameworks.
The paper tackles the challenge of applying Wasserstein Distributionally Robust Optimization (DRO) to ensure individual fairness in learning problems with causal structures and sensitive attributes, resulting in a reformulated DRO problem with a closed-form regularizer and finite sample error bounds for robust learning.
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.