# Towards Optimal Inventory Control under Censored Demand: A Biased Sample-Average Approximation Approach

arXiv: https://arxiv.org/abs/2609.39397 · HTML: https://mlsanity.com/paper/2609.39397/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 60 references that are in the map.
- First posted on arXiv 30 Sep 2026.

## Builds on (most cited first, 11 of 11)

- [Nearly Minimax Optimal Offline Reinforcement Learning with Linear Function Approximation: Single-Agent MDP and Markov Game](https://mlsanity.com/paper/2205.15512/) (2022)
- [How Big Should Your Data Really Be? Data-Driven Newsvendor: Learning One Sample at a Time](https://mlsanity.com/paper/2107.02742/) (2021)
- [VC Theory for Inventory Policies](https://mlsanity.com/paper/2404.11509/) (2024)
- [Learning to Order for Inventory Systems with Lost Sales and Uncertain Supplies](https://mlsanity.com/paper/2207.04550/) (2022)
- [Regret Optimality of Sample Average Approximation for Data-Driven Newsvendor Problems: A General Optimization Perspective](https://mlsanity.com/paper/2407.04900/) (2024)
- [Reinforcement Learning in MDPs with Information-Ordered Policies](https://mlsanity.com/paper/2508.03904/) (2025)
- [The Data-Driven Censored Newsvendor Problem](https://mlsanity.com/paper/2412.01763/) (2024)
- [Learning When to Restart: Nonstationary Newsvendor from Uncensored to Censored Demand](https://mlsanity.com/paper/2509.18709/) (2025)
- [A Minibatch-SGD-Based Learning Meta-Policy for Inventory Systems with Myopic Optimal Policy](https://mlsanity.com/paper/2408.16181/) (2024)
- [Survey of Data-driven Newsvendor: Unified Analysis and Spectrum of Achievable Regrets](https://mlsanity.com/paper/2409.03505/) (2024)
- [What is the Value of Censored Data? An Exact Analysis for the Data-driven Newsvendor](https://mlsanity.com/paper/2602.16842/) (2026)

## Abstract (arXiv)

We study data-driven multi-period lost-sales inventory control under censored demand, where a stockout reveals only that demand exceeded the stocking level. We develop a unified, model-based framework for policy learning from censored data, built on a new cost decomposition for base-stock policies and a biased sample-average approximation (SAA) approach. The cost decomposition allows us to propose a new coverage condition under which censored observations are informative enough for sample-efficient policy learning. Guided by this coverage condition, we design two biased SAA algorithms: an upper-biased one that achieves near-optimal sample complexity under the offline coverage condition, and a lower-biased one that actively generates the required coverage and achieves near-optimal regret online. More broadly, this biased SAA approach provides a general principle for implementing pessimism and optimism under censored feedback, which may be of independent interest.