Variable Selection for Feature-Based Newsvendor

Feature-based newsvendor models use observable covariates to tailor inventory decisions, aiming to balance holding and shortage costs under demand uncertainty. However, high-dimensional feature sets often hinder interpretability and inflate data collection and implementation costs. This paper studies variable selection for the feature-based newsvendor problem under a hard cardinality constraint on the number of selected features. We formulate the resulting $\ell_0$-constrained empirical newsvendor problem with $\ell_2$-regularization, establish its computational hardness, and develop a mixed-integer second-order cone programming reformulation that strengthens the standard Big-$M$ formulation. To enable scalability beyond exact optimization, we develop a randomized-rounding algorithm with a bi-criteria guarantee and a greedy heuristic. Statistically, we provide theoretical analysis of the resulting sparse policy estimator, including finite-sample estimation error, out-of-sample risk bounds, and support recovery guarantees. Extensive experiments on both synthetic and real data illustrate the computational and statistical trade-offs among various baselines. Our results demonstrate that the proposed variable selection framework achieves competitive out-of-sample operational costs while using substantially fewer covariates.

How much Data do We Need? Sequential Data Collection for Stochastic Programming

Data-driven optimization often requires collecting data to estimate uncertain model parameters before solving the underlying decision problem. In practice, however, data acquisition may incur non-negligible costs, making it critical to determine when to stop additional data collection. In this paper, we study an optimal stopping problem for sequential data collection in stochastic optimization under parameter uncertainty. We propose a benefit-driven stopping framework that balances information gain and sampling cost. We model the unknown distribution parameter within a Bayesian learning framework and update beliefs sequentially as new observations are collected. At each iteration, the decision maker evaluates the expected marginal benefit of additional data relative to the unit sampling cost and determines whether to continue sampling or stop and implement the optimization decision. Based on this framework, we develop several stopping policies. The proposed policies are evaluated through a newsvendor problem with exponentially distributed demand. Numerical experiments compare the policies with fixed-budget and hindsight benchmark strategies. The results show that benefit-driven stopping rules can substantially reduce unnecessary data collection while achieving near-optimal decision performance, demonstrating the effectiveness of adaptive stopping in data-driven optimization.