An Online Mirror Descent Learning Algorithm for Multiproduct Inventory Systems

Learning to Manage Multiproduct Inventory from Incomplete Demand Signals Managing inventory across different products within limited warehouse space is a central challenge in retail and supply chain operations, especially when demand is unknown and lost-sales data are missing. This problem becomes even harder as product assortments grow larger. In “An Online Mirror Descent Learning Algorithm for Multiproduct Inventory Systems,” Guo et al. develop the online mirror descent learning algorithm (OMELET), a scalable online learning algorithm that dynamically adjusts replenishment decisions using observed sales data. The method builds on mirror descent with cyclic updates to efficiently handle high-dimensional product menus. The authors show that the algorithm’s regret grows only logarithmically with the number of products, a significant theoretical improvement over existing approaches. Extensive numerical experiments using empirical data confirm that OMELET not only outperforms existing state-of-the-art methods but also, translates into practical, actionable insights for managers making real-time inventory decisions.