Distributionally Fair Stochastic Optimization using Wasserstein Distance


    Department of Decisions, Operations and Technology &

    Department of Systems Engineering and Engineering Management

                       The Chinese University of Hong Kong


Date: Monday, May 27, 4:00 pm – 5:30 pm

Venue: ERB 513, The Chinese University of Hong Kong.

Title: Distributionally Fair Stochastic Optimization using Wasserstein Distance 

Speaker: Prof. Weijun Xie, H. Milton Stewart School of Industrial and Systems Engineering, Georgia Tech



A traditional stochastic program under a finite population typically seeks to optimize efficiency by maximizing the expected profits or minimizing the expected costs, subject to a set of constraints. However, implementing such optimization-based decisions can have varying impacts on individuals, and when assessed using the individuals' utility functions, these impacts may differ substantially across demographic groups delineated by sensitive attributes, such as gender, race, age, and socioeconomic status. As each group comprises multiple individuals, a common remedy is to enforce group fairness, which necessitates the measurement of disparities in the distributions of utilities across different groups. This paper introduces the concept of Distributionally Fair Stochastic Optimization (DFSO) based on the Wasserstein fairness measure. The DFSO aims to minimize distributional disparities among groups, quantified by the Wasserstein distance, while adhering to an acceptable level of inefficiency. Our analysis reveals that: (i) the Wasserstein fairness measure recovers the demographic parity fairness prevalent in binary classification literature; (ii) this measure can approximate the well-known Kolmogorov-Smirnov fairness measure with considerable accuracy; and (iii) despite DFSO's biconvex nature, the epigraph of the Wasserstein fairness measure is generally Mixed-Integer Convex Programming Representable (MICP-R). Additionally, we introduce two distinct lower bounds for the Wasserstein fairness measure: the Jensen bound, applicable to the general Wasserstein fairness measure, and the Gelbrich bound, specific to the type-2 Wasserstein fairness measure. We establish the exactness of the Gelbrich bound and quantify the theoretical difference between the Wasserstein fairness measure and the Gelbrich bound.



Dr. Weijun Xie is the Coca-Cola Foundation Early Career Professor and Assistant Professor in the H. Milton Stewart School of Industrial and Systems Engineering at Georgia Tech. Dr. Xie obtained his Ph.D. in Operations Research at the Georgia Institute of Technology in 2017. His research interests are theory and applications of stochastic, discrete, and convex optimization. His works have received multiple awards, including the 2022 New Investigator Award from the Virginia Space Grant Consortium (NASA), the 2021 NSF CAREER Award, and the Winner of the 2020 INFORMS Young Researchers Paper Prize. He currently serves as Associate Editor of Operations Research, Mathematical Programming, and the Journal of Global Optimization.


Everyone is welcome to attend the talk!

SEEM-5202 Website:


Monday, May 27, 2024 - 16:00