An efficient learning framework for multiproduct inventory systems with customer choices
针对顾客购买受产品可得性影响的多产品库存系统，提出一种基于UCB的学习框架，利用两种改进思路加速学习，在超过1000个候选策略时50期内平均遗憾约15%。
We consider a periodic‐review multiproduct inventory system where customers' purchasing decisions are affected by the product availabilities. Demands need to be learned on the fly, through the partial and censored feedback of customers. For this learning problem, if one ignores the inventory dynamic and treats it as a multiarmed bandit problem and directly applies some existing algorithms, for example, the upper confidence bound (UCB) algorithm, the convergence can be extremely slow due to the high‐dimensionality of the policy space. We propose a UCB‐based learning framework that utilizes the sales information based on two improvement ideas. We illustrate how these two ideas can be incorporated by considering two specific systems: (1) multiproduct inventory system with stock‐out substitutions, (2) multiproduct inventory assortment problem for urban warehouses. We develop improved UCB algorithms for both systems, using the two improvements. For both systems, the algorithm can achieve a tight worst‐case convergence rate (up to a logarithmic term) on the planning horizon <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:semantics definitionURL="" encoding=""> <mml:mi>T</mml:mi> <mml:annotation encoding="">$T$</mml:annotation> </mml:semantics> </mml:math> . Extensive numerical experiments are conducted to demonstrate the efficiency of the improved UCB algorithms for the two systems. In the experiments, when there are more than 1000 candidate policies to choose from, the algorithms can achieve around <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:semantics definitionURL="" encoding=""> <mml:mrow> <mml:mn>15</mml:mn> <mml:mo>%</mml:mo> </mml:mrow> <mml:annotation encoding="">$15\%$</mml:annotation> </mml:semantics> </mml:math> average expected regret within 50 periods and continue to steadily improve as time increases.