Contextual Optimization under Covariate Shift: A Robust Approach by Intersecting Wasserstein Balls
Professor WANG Chun
Associate Professor
Department of Management Science and Engineering
Tsinghua University School of Economics and Management
In contextual optimization, a decision-maker (DM) relies on historical data concerning uncertain parameters and covariates, yet they lack precise knowledge of the underlying distributions. Given a new test covariate, a typical decision-making process is “estimate-then-optimize”, where the DM first estimates a conditional distribution from the training samples and then chooses decisions to minimize the expected cost over this estimation. However, when the covariate distribution differs between the training and test sets, known as covariate shift, the upstream estimation may yield inaccurate predictions for test covariates far from the training samples, and therefore the downstream optimization will likely produce poor decisions. To address this challenge, we introduce a new approach within the distributionally robust optimization (DRO) framework, designated as IW-DRO, where we propose a novel ambiguity set defined as the intersection of two Wasserstein balls, with the centers of these balls constructed using appropriate parametric and nonparametric estimators, respectively. We offer a computationally tractable reformulation of the IW-DRO problem and also develop an approximate algorithm tailored for large-scale problems with high computational efficiency. We provide statistical guarantees for IW-DRO in the presence of covariate shift by analyzing the measure concentration of the estimators. In particular, we show that IW-DRO can achieve better cost performance than the corresponding single Wasserstein-ball DRO models. Through extensive numerical experiments with both synthetic and real data, we demonstrate that IW-DRO outperforms various benchmark policies in a covariate-shift environment.
Dr. Chun Wang is an associate professor in the Department of Management Science and Engineering at the School of Economics and Management, Tsinghua University. His research interests include: theoretical and computational methodologies in dynamic programming, stochastic control, robust optimization, and machine learning, and their applications in inventory management, revenue management, finance engineering, and sports analytics. He earned his Ph.D. in operations research from Columbia University.
