# Thompson Sampling for Repeated Newsvendor

arXiv: https://arxiv.org/abs/2502.09900 · HTML: https://mlsanity.com/paper/2502.09900/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 20 references that are in the map.
- First posted on arXiv 14 Feb 2025.

## Builds on (most cited first, 4 of 4)

- [Learning to Optimize Via Posterior Sampling](https://mlsanity.com/paper/1301.2609/) (2013)
- [An Information-Theoretic Analysis of Thompson Sampling](https://mlsanity.com/paper/1403.5341/) (2014)
- [Learning in structured MDPs with convex cost functions: Improved regret bounds for inventory management](https://mlsanity.com/paper/1905.04337/) (2019)
- [Bayesian Design Principles for Frequentist Sequential Learning](https://mlsanity.com/paper/2310.00806/) (2023)

## Built on by (most cited first, 1 of 1)

- [In-Context Learning for Data-Driven Censored Inventory Control](https://mlsanity.com/paper/2605.14840/) (2026)

## Abstract (arXiv)

In this paper, we investigate the performance of Thompson Sampling (TS) for online learning with censored feedback, focusing primarily on the classic repeated newsvendor model--a foundational framework in inventory management--and demonstrating how our techniques can be naturally extended to a broader class of problems. We first model demand using a Weibull distribution and initialize TS with a Gamma prior to dynamically adjust order quantities. Our analysis establishes optimal (up to logarithmic factors) frequentist regret bounds for TS without imposing restrictive prior assumptions. More importantly, it yields novel and highly interpretable insights on how TS addresses the exploration-exploitation trade-off in the repeated newsvendor setting. Specifically, our results show that when past order quantities are sufficiently large to overcome censoring, TS accurately estimates the unknown demand parameters, leading to near-optimal ordering decisions. Conversely, when past orders are relatively small, TS automatically increases future order quantities to gather additional demand information. Then, we extend our analysis to general parametric distribution family and provide proof for Bayesian regret. Extensive numerical simulations further demonstrate that TS outperforms more conservative and widely-used approaches such as online convex optimization, upper confidence bounds, and myopic Bayesian dynamic programming.