主 题:Multi-Sample U-Process for Data-Driven Multi-Stage Inventory Policies基于数据驱动的多阶段库存策略的Multi-Sample U-Process
主讲人:新加坡国立大学叶志盛副教授
主持人:统计学院林华珍教授
时间:2024年6月4日(周二)下午4:00-5:00
举办地点:柳林校区弘远楼408会议室
主办单位:统计研究中心和统计学院 科研处
主讲人简介:
Dr. Ye received a joint B.E. (2008) in Material Science & Engineering, and Economics from Tsinghua University. He received a Ph.D. degree from National University of Singapore. He is currently an Associate Professor and Dean's Chair in the Department of Industrial Systems Engineering & Management at National University of Singapore. His research areas include industrial statistics, reliability engineering, and data-driven operations management. His work has been published in flagship journals in statistics, reliability, and operations management, including Bernoulli, Biometrics, Biometrika, JASA, JMLR, JRSS-B, JRSS-C, Technometrics, JQT, IISE Trans, IEEE-TIT, IEEE-TAC, MSOM and POMS.
Dr. Ye于2008年在清华大学获得材料科学与工程及经济学的双学士学位,并在新加坡国立大学获得博士学位。目前,他是新加坡国立大学工业系统工程与管理系的副教授兼院长讲席教授。他的研究领域包括工业统计、可靠性工程和数据驱动的运营管理。他的研究成果发表在统计学、可靠性和运营管理领域的旗舰期刊上,包括《Bernoulli》、《Biometrics》、《Biometrika》、《JASA》、《JMLR》、《JRSS-B》、《JRSS-C》、《Technometrics》、《JQT》、
、《IISE Trans》、《IEEE-TIT》、《IEEE-TAC》、《MSOM》、《POMS》。
内容简介:
We study periodic review stochastic inventory control in the data-driven setting, in which the retailer makes ordering decisions based only on historical demand observations without any knowledge of the probability distribution of the demand. Since an (s, S)-policy is optimal when the demand distribution is known, we investigate the statistical properties of the data-driven (s, S)-policy obtained by recursively computing the empirical cost-to-go functions (called DP-based estimator). This estimator is inherently challenging to analyze because the recursion induces propagation of the estimation error backward in time. In this work, we establish asymptotic properties of this data-driven policy by fully accounting for the error propagation. First, we rigorously show the consistency of the estimated parameters by filling in some gaps (due to unaccounted error propagation) in the existing studies. On the other hand, empirical process theory cannot be directly applied to show asymptotic normality since the empirical cost-to-go functions for the estimated parameters are not i.i.d. sums, again due to the error propagation. Our main methodological innovation comes from an asymptotic representation for multi-sample U-processes in terms of i.i.d. sums. This representation enables us to apply empirical process theory to derive the influence functions of the estimated parameters and establish joint asymptotic normality. Based on these results, we also propose an entirely data-driven estimator of the optimal expected cost and we derive its asymptotic distribution. Beyond deriving the asymptotic distribution of our DP-based estimators, we further investigate the semiparametric efficiency of the proposed estimators. We show that the asymptotic variances of DP-based estimators match the statistical lower bound and so the proposed estimators are asymptotically efficient.
主讲人研究了数据驱动环境下的周期性审查随机库存控制,在这种环境中,零售商仅根据历史需求观察值做出订货决策,而无需了解需求的概率分布。由于在需求分布已知的情况下,(s, S)-策略是最优的,主讲人研究了通过递归计算经验成本函数(称为基于DP的估计器)得到的数据驱动(s, S)-策略的统计性质。由于递归导致估计误差在时间上的传播,这个估计器本质上具有分析上的挑战。在这项工作中,主讲人通过完全考虑误差传播,建立了这种数据驱动策略的渐近性质。首先,主讲人通过填补现有研究中因未考虑误差传播而存在的一些空白,严格证明了估计参数的一致性。另一方面,由于估计参数的经验成本函数不是独立同分布的和,经验过程理论无法直接应用于证明渐近正态性,这也是由于误差传播。主讲人的主要方法创新来自于将多样本U-过程表示为独立同分布的和的渐近表示。这一表示能够应用经验过程理论,推导估计参数的影响函数并建立联合渐近正态性。基于这些结果,主讲人还提出了一个完全数据驱动的最优期望成本估计器,并推导了其渐近分布。除了推导基于DP的估计器的渐近分布外,主讲人还进一步研究了所提估计器的半参数效率。结果表明,基于DP的估计器的渐近方差与统计下界一致,因此所提估计器是渐近有效的。