Marrying Stochastic Gradient Descent with Bandits: Learning Algorithms for Inventory Systems with Fixed Costs

• 成果类型: Article
• 署名作者: Yuan, Hao; Luo, Qi; Shi, Cong
• 署名单位: University of Michigan System; University of Michigan
• 刊物名称: MANAGEMENT SCIENCE
• ISSN/ISSBN: 0025-1909
• DOI: 10.1287/mnsc.2020.3799
• 发表日期: 2021
• 页码: 6089-6115
• 关键词: INVENTORY; fixed costs; censored demand; learning algorithms; Nonparametric; Regret Analysis

摘要

We consider a periodic-review single-product inventory system with fixed cost under censored demand. Under full demand distributional information, it is well known that the celebrated (s, S) policy is optimal. In this paper, we assume the firm does not know the demand distribution a priori and makes adaptive inventory ordering decisions in each period based only on the past sales (a.k.a. censored demand). Our performance measure is regret, which is the cost difference between a feasible learning algorithm and the clairvoyant (full-information) benchmark. Compared with prior literature, the key difficulty of this problem lies in the loss of joint convexity of the objective function as a result of the presence of fixed cost. Wedevelop the first learning algorithm, termed the (d, S) policy, that combines the power of stochastic gradient descent, bandit controls, and simulation-based methods in a seamless and nontrivial fashion. We prove that the cumulative regret is O(log T root T), which is provably tight up to a logarithmic factor. We also develop several technical results that are of independent interest. We believe that the developed framework could be widely applied to learning other important stochastic systems with partial convexity in the objectives.