arXiv:2502.09900cs.LG2025-02被引 1

用汤普森采样解决库存预测中的反馈缺失问题,实现更优订货决策。

Thompson Sampling for Repeated Newsvendor

  • 基于威布尔分布与伽马先验,动态调整订货量。
  • 在历史订货量足够大时,能准确估计需求参数,接近最优。
  • 自动平衡探索与利用,适合数据稀疏场景下的智能库存管理。

本文研究汤普森采样(Thompson Sampling, TS)在带截断反馈的在线学习中的表现,聚焦经典的重复报童模型——库存管理的基础框架,并展示方法可推广至更广泛的问题。我们采用威布尔分布建模需求,以伽马分布作为先验初始化TS,动态调节订货量。分析建立了无需严格先验假设的最优(对数因子内)频率论后悔界。结果揭示了TS如何在重复报童设定中有效处理探索-利用权衡:当历史订货量足够大、能克服截断影响时,TS能准确估计未知需求参数,实现近最优订货;当历史订货较小,则自动提高未来订货量以获取更多需求信息。进一步将分析扩展至一般参数化分布族,并给出贝叶斯后悔界的证明。大量数值模拟表明,相较于更保守且广泛应用的方法(如在线凸优化、上置信界、贪心贝叶斯动态规划),TS表现更优。

原文摘要 · Abstract (English)

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.

库存优化贝叶斯学习在线学习汤普森采样

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