Advances in computational power and AI have increased interest in reinforcement learning approaches to inventory management. This paper provides a theoretical foundation for these approaches and investigates the benefits of restricting to policy structures that are well-established by decades of inventory theory. In particular, we prove generalization guarantees for learning several well-known classes of inventory policies, including base-stock and (s, S) policies, by leveraging the celebrated Vapnik-Chervonenkis (VC) theory. We apply the concepts of the Pseudo-dimension and Fat-shattering dimension from VC theory to determine the generalizability of inventory policies, that is, the difference between an inventory policy's performance on training data and its expected performance on unseen data. We focus on a classical setting without contexts, but allow for an arbitrary distribution over demand sequences and do not make any assumptions such as independence over time. We corroborate our supervised learning results using numerical simulations. Managerially, our theory and simulations translate to the following insights. First, there is a principle of "learning less is more" in inventory management: depending on the amount of data available, it may be beneficial to restrict oneself to a simpler, albeit suboptimal, class of inventory policies to minimize overfitting errors. Second, the number of parameters in a policy class may not be the correct measure of overfitting error: in fact, the class of policies defined by T time-varying base-stock levels exhibits a generalization error comparable to that of the two-parameter (s, S) policy class. Finally, our research suggests situations in which it could be beneficial to incorporate the concepts of base-stock and inventory position into black-box learning machines, instead of having these machines directly learn the order quantity actions.

翻译：计算能力的提升与人工智能的发展激发了人们对强化学习在库存管理中应用的兴趣。本文为这些方法奠定了理论基础，并探讨了将策略限制在经数十年库存理论验证的结构中所带来的优势。具体而言，我们通过运用著名的Vapnik-Chervonenkis（VC）理论，证明了学习包括基本库存策略和(s,S)策略在内的几类经典库存策略的泛化保证。我们应用VC理论中的伪维度和脂肪破碎维度概念来确定库存策略的可泛化性，即库存策略在训练数据上的表现与对未见数据的期望表现之间的差异。我们聚焦于无情境的传统设定，但允许需求序列服从任意分布，且不依赖时间独立等假设。通过数值模拟验证了监督学习结果。从管理角度而言，理论与模拟可转化为以下洞见：第一，库存管理存在"少学即多学"原则——根据可用数据量，限制使用更简单（即使非最优）的库存策略类别可最小化过拟合误差；第二，策略类别的参数数量并非衡量过拟合误差的正确指标——实际上，由T个时变基本库存水平定义的策略类别的泛化误差与双参数(s,S)策略类别相当；最后，研究表明将基本库存与库存位置概念融入黑箱学习机器，而非让机器直接学习订货量动作，可能更有利于特定情境下的决策优化。