Overcoming Demand Censoring through Randomization for Risk-Sensitive Newsvendor Learning
Abstract
We study online newsvendor learning with bounded demand, censored observations, and convex nonlinear shortage costs. Because stockouts can conceal the shortage magnitudes needed by gradient-based algorithms, we use randomized ordering to construct unbiased subgradient estimates. We characterize admissible randomization distributions within this framework and develop an online inventory policy that combines the resulting subgradient estimates with gradient-based updates. Our regret analysis quantifies the cost of randomization via the estimation variance and an additional loss term. We characterize the randomization distributions that minimize this objective. For piecewise-linear shortage costs, the optimal distribution is computed through a linear-time recursion; for costs with bounded curvature density, it is characterized by a scalar ordinary differential equation. The policy achieves expected regret of O(T2/3) against the best fixed order in hindsight over T periods. Under independent demand and suitable curvature of expected losses, the bound improves to O(√T). Matching minimax lower bounds establish rate optimality over the corresponding classes with a fixed marginal-cost bound. Both rates extend to nonperishable inventory under uniformly positive conditional expected demand. Numerical experiments on synthetic and retail data show improvements over alternative policies using censored observations.
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BibTeX
@misc{wang2026overcoming,
title = {{Overcoming Demand Censoring through Randomization for Risk-Sensitive Newsvendor Learning}},
author = {Zhengchao Wang and Nam Ho-Nguyen},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.02267},
eprint = {2611.02267},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.02267},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - Overcoming Demand Censoring through Randomization for Risk-Sensitive Newsvendor Learning
AU - Zhengchao Wang
AU - Nam Ho-Nguyen
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.02267
UR - https://arxiv.org/abs/2611.02267
AB - We study online newsvendor learning with bounded demand, censored observations, and convex nonlinear shortage costs. Because stockouts can conceal the shortage magnitudes needed by gradient-based algorithms, we use randomized ordering to construct unbiased subgradient estimates. We characterize admissible randomization distributions within this framework and develop an online inventory policy that combines the resulting subgradient estimates with gradient-based updates. Our regret analysis quantifies the cost of randomization via the estimation variance and an additional loss term. We characterize the randomization distributions that minimize this objective. For piecewise-linear shortage costs, the optimal distribution is computed through a linear-time recursion; for costs with bounded curvature density, it is characterized by a scalar ordinary differential equation. The policy achieves expected regret of O(T^2/3) against the best fixed order in hindsight over T periods. Under independent demand and suitable curvature of expected losses, the bound improves to O(√T). Matching minimax lower bounds establish rate optimality over the corresponding classes with a fixed marginal-cost bound. Both rates extend to nonperishable inventory under uniformly positive conditional expected demand. Numerical experiments on synthetic and retail data show improvements over alternative policies using censored observations.
ER -