A Hybrid Sampling Based and Gradient Descent Method with Applications in Inventory Management

In this paper, we consider a class of inventory management applications where the distribution of the underlying demand is unknown and the manager must make an inventory-ordering decision in each period based only on the past demand data. The standard performance measure is regret, which is the cost difference between a learning algorithm and the clairvoyant (full-information) benchmark. When the benchmark is chosen to be the (full-information) optimal policy, we propose a new nonparametric learning algorithm that combines the Sample Average Approximation (SAA) approach and the Stochastic Gradient Descent (SGD) method to admit a regret bound of $\mathcal{O}(\sqrt{K})$ ($K$ is the planning horizon), which matches the theoretical lower bound. We demonstrate the usefulness of the algorithm by applying it to two classic inventory problems: dual-sourcing and two-echelon inventory problems, under the assumption that the manager does not know the demand distributions and has access only to historical data. We also conduct numerical experiments to demonstrate the effectiveness of our proposed algorithms