Recently, the paper “Feature-Rich, Data-Private: A Sparse Learning Framework for the High-Dimensional Newsvendor,” co-authored by Professor Jinyuan Chang and Postdoctoral Fellow Lin Yang from the team, Associate Professor Yichen Zhang of Purdue University, and Associate Professor Wenxin Zhou of the University of Illinois Chicago, was officially accepted for publication in Operations Research, a leading international journal in management science and operations research.
Abstract
Firms leveraging high-dimensional data for the feature-based newsvendor problem face a dual challenge: the operational risk of learning ineffective policies from a vast feature space and the strategic risk of leaking sensitive data. Standard privacy mechanisms are ill-suited for this context, as the noise required for privacy often scales with the ambient dimension, overwhelming the sparse signals that drive demand. To resolve this tension, we develop a differentially private algorithm that synergistically combines a noisy variant of Iterative Hard Thresholding with convolution-based smoothing of the newsvendor cost function. By carefully calibrating noise within the hard-thresholding step, our method simultaneously enforces model sparsity and provides rigorous privacy guarantees, while the smoothed surrogate stabilizes the iterative optimization process. We establish non-asymptotic error bounds that characterize the trade-offs among privacy, sparsity, feature dimension, and sample size. Crucially, our analysis reveals that the algorithm’s performance depends on the intrinsic sparsity (s) rather than the ambient dimension (p). We prove that the excess operational cost (regret) converges at an accelerated rate of O(sn^{-1}\log p), a significant improvement over the standard rate O(p^{1/2}n^{-1/2}) for non-smooth problems. These theoretical insights provide a principled justification for aggressive feature engineering, enabling firms to leverage complex data sources without incurring a dimensionality penalty. An empirical study using real-world retail data corroborates our theory, demonstrating that the proposed framework provides a robust solution for achieving both operational efficiency and data security in modern inventory management.
Author Introduction
Jinyuan Chang is a Guanghua Chair Professor at Southwestern University of Finance and Economics, Executive Dean of the Institute for Interdisciplinary Innovation in Statistics, and Executive Director of the Joint Laboratory of Data Science and Business Intelligence. His main research interests include complex data analysis.
Lin Yang is a Postdoctoral Fellow at the Joint Laboratory of Data Science and Business Intelligence, Southwestern University of Finance and Economics. His main research interests include high-dimensional time series analysis and functional data analysis.
Yichen Zhang is an Associate Professor at Purdue University. His research interests include online inference for stochastic systems, distributed inference under data heterogeneity, and data-driven optimization for complex operations systems.
Wenxin Zhou is an Associate Professor at the University of Illinois Chicago. His research interests include high-dimensional statistics and robust inference, nonparametric learning and modern machine learning methods, deep learning and neural network theory, as well as quantile regression and expected shortfall regression.
