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

2025-09-30

AI Summary

This work addresses individual fairness under unknown causal relationships between sensitive attributes and decisions. We propose a novel framework integrating Wasserstein distributionally robust optimization (DRO) with causal inference—without requiring a pre-specified structural causal model. To this end, we are the first to embed Wasserstein DRO directly into individual fairness constraints: counterfactual distributional shifts are modeled via a Wasserstein ball around the observed distribution, and the resulting min-max optimization is reformulated—via duality—into a differentiable regularized learning problem. Theoretically, we derive a finite-sample error bound for learning under unknown causal structure. Empirically, our method simultaneously enhances individual fairness and robustness to distributional shifts, while maintaining computational efficiency.

Technology Category

• Machine Learning: Causal Learning
• Reasoning under Uncertainty: Causality
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

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.

Problem

• Applying Wasserstein DRO to address individual fairness with causal structures
• Converting DRO problems into tractable forms using dual formulations
• Providing finite sample bounds for DRO with estimated causal models

Innovation

• Dual formulation converts DRO to tractable form
• Closed-form regularizer eliminates min-max optimization
• Finite sample bounds with estimated causal structures