Feature-Rich, Data-Private: A Sparse Learning Framework for the High-Dimensional Newsvendor

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, because 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, whereas the smoothed surrogate stabilizes the iterative optimization process. We establish nonasymptotic error bounds that characterize the tradeoffs among privacy, sparsity, feature dimension, and sample size. Crucially, our analysis reveals that the algorithm’s performance depends on the sparsity budget (s) rather than the ambient dimension (p). We prove that the excess operational cost (regret) converges at an accelerated rate of $O(s{n}^{-1}\text{log} p)$, a significant improvement over the standard rate $O(p^{1/2}{n}^{-1/2})$ for nonsmooth problems. These theoretical insights provide a principled justification for extensive 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.

Funding: J. Chang and L. Yang were supported in part by the National Natural Science Foundation of China [Grants 72495122, 72621003, and 72125008]. L. Yang was also supported in part by the China Postdoctoral Science Foundation [Grant 2026M793402].

Supplemental Material: All supplemental materials, including the code, data, and files required to reproduce the results, are available at https://doi.org/10.1287/opre.2025.2370.