【鲁棒与随机优化系列讲座(二)】 Feature-Based Nonparametric Inventory Control with Censored Demand

时间:2021-04-07         阅读:

光华讲坛——鲁棒与随机优化系列讲座第二期

主题:【鲁棒与随机优化系列讲座(二)】Feature-Based Nonparametric Inventory Control with Censored Demand

主讲人上海交通大学 荣鹰教授

主持人工商管理学院 徐亮教授

时间2021年4月15日(星期四)14:00-15:00

直播平台及会议ID腾讯会议 会议ID:655 466 814

主办单位:工商管理学院 科研处

主讲人简介:

荣鹰博士现任上海交通大学安泰经济与管理学院教授。他于2010年8月回国执教于上海交通大学,此前在美国加州大学伯克利分校和里海大学从事博士后科研工作,并在上海交通大学和美国里海大学分别获学士、硕士和博士学位。荣鹰教授主要研究领域为服务运营管理、零售运营管理、新兴商业模型的运作以及数据驱动的优化模型。研究成果发表在Management Science、Operations Research、Manufacturing & Service Operations Management、Production and Operations Management、Naval Research Logistics、IIE Transactions等国际学术刊物上。荣鹰教授是2015年度国家优秀青年科学基金和2020年度国家杰出青年科学基金获得者并且多次获得过国际奖项,其中包括两度MSOM最佳论文奖,TSL最佳论文奖和INFORMS Energy, Natural Resources & Environment Young Researcher Prize。

内容提要:

We study stochastic periodic-review inventory systems with lost sales, where the decision maker has no access to the true demand distribution a priori and can only observe historical sales data (referred to as censored demand) and feature information about the demand. We propose two feature-based nonparametric inventory algorithms called the feature-based adaptive inventory algorithm and the dynamic shrinkage algorithm. Both algorithms are based on the stochastic gradient descent method. We measure the performance of the proposed algorithms through the average expected regret in finite periods: that is, the difference between the cost of our algorithms and that of a clairvoyant optimal policy with access to information, which is acting optimally. We show that the average expected cost incurred under both algorithms converges to the clairvoyant optimal cost at some rate.However, the feature-based adaptive inventory algorithm results in high volatility in the stochastic gradients, which hampers the initial performance of regret. The dynamic shrinkage algorithm uses a shrinkage parameter to adjust the gradients, which significantly improves the initial performance. The idea of dynamic shrinkage for the stochastic gradient descent method builds on a fundamental insight known as the bias-variance trade-off.

本文研究了具有销售损失的定期盘点随机系统,决策者无法先验地获得真实的需求分配,只能观察历史销售数据(即缺货未知的需求)和需求特征信息。文中提出两种基于特征的非参数库存算法,分别称为基于特征的自适应库存算法和动态收缩算法,两种算法均基于随机梯度下降法。通过有限时期内的平均期望后悔值来衡量所提出的算法性能:即所提出算法的成本与采用最佳信息获取能力的最优策略成本之间的差异。结果表明,在两种算法下产生的平均期望成本以特定的比率收敛到最优成本。然而,基于特征的自适应库存算法导致随机梯度的高波动性,从而阻碍了初始性能的表现。动态收缩算法使用收缩参数来调整梯度,从而显着提高了初始性能。随机梯度下降法的动态收缩思想,建立在权衡偏差-方差的基本观点之上。