Marrying Stochastic Gradient Descent With Bandits
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Marrying Stochastic Gradient Descent with Bandits
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 decision in each period based only on the past sales (a.k.a. censored demand) data. The standard 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, due to the presence of fixed cost. We develop a nonparametric learning algorithm termed the $( delta, S)$ policy that combines the powers of stochastic gradient descent, bandit controls, and simulation-based methods in a seamless and non-trivial fashion. We prove that the cumulative regret is $O( log T sqrt{T})$, which is provably tight up to a logarithmic factor. We also develop several technical results that are of independent interest. We believe that the framework developed could be widely applied to learning other important stochastic systems with partial convexity in the objectives.
The Elements of Joint Learning and Optimization in Operations Management
This book examines recent developments in Operations Management, and focuses on four major application areas: dynamic pricing, assortment optimization, supply chain and inventory management, and healthcare operations. Data-driven optimization in which real-time input of data is being used to simultaneously learn the (true) underlying model of a system and optimize its performance, is becoming increasingly important in the last few years, especially with the rise of Big Data.
Research Handbook on Inventory Management
Author: Jing-Sheng J. Song
language: en
Publisher: Edward Elgar Publishing
Release Date: 2023-08-14
This comprehensive Handbook provides an overview of state-of-the-art research on quantitative models for inventory management. Despite over half a century’s progress, inventory management remains a challenge, as evidenced by the recent Covid-19 pandemic. With an expanse of world-renowned inventory scholars from major international research universities, this Handbook explores key areas including mathematical modelling, the interplay of inventory decisions and other business decisions and the unique challenges posed to multiple industries.