联合优化价格与库存，实现动态定价中需求学习与履约成本的协同控制。
Online Pricing and Allocation with Demand Learning and Fulfillment Cost
- 通过反事实转换学习需求，结合乐观下界决策联合优化价格与库存。
- 在理性多面体库存集上实现多项式时间求解，理论证明为 $ ilde{O}( oot{T}{})$ 误差。
- 适用于需兼顾价格调整与物流履约的电商或供应链场景。
我们研究卖家在每期同时决定库存水平和统一价格，并通过下游分配机制满足实际需求的在线学习问题。主要挑战在于：价格会影响需求分布，从而改变运输线性规划结构，导致全局目标函数非凸且不可微。为此，我们提出 OCSAA 算法，利用反事实翻译处理需求观测，通过下置信区间乐观策略生成联合（价格, 库存）决策。该算法在有理多面体库存集上具有多项式时间加性精度实现。我们证明了高概率 $ ilde{O}( oot{T}{})$ 的后悔界，并建立了匹配 $T$ 的信息论下界。结果表明，统计学习方法可有效融合复杂运筹学问题。
原文摘要 · Abstract (English)
We study online learning for a seller that jointly chooses per-period inventory positions and a uniform price, then fulfills realized demand through a downstream allocation. The main difficulty is not only demand learning: the price shifts demand and reshapes the transportation LP, making the population objective globally non-convex and non-smooth. To solve this problem, we propose OCSAA, an algorithm that exploits demand observations through counterfactual translation and proposes joint (price, inventory) decisions through lower-confidence optimism. OCSAA admits a polynomial-time additive-accuracy implementation for rational-polytope inventory sets. We prove a high-probability $\widetilde O(\sqrt T)$ regret guarantee and establish a matching-in-$T$ information-theoretic lower bound. Our results illustrate an effective integration of statistical learning methodologies with complex operations research problems.
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