Comparing Online Learning Algorithms to Stochastic Approaches for the Multi-Period Newsvendor Problem

The multi-period newsvendor problem describes the dilemma of a newspaer salesman-how many papers should he purchase each day to resell, when he doesn't know the demand? We develop approaches for this well known problem based on two machine learning algorithms: Weighted Majority of Warmuth and Littlestone, and Follow the Perturbed Leader of Kalai and Vempala. With some modified analysis, it isn't hard to show theoretical bounds for our modified versions of these algorithms. More importantly, we test the algorithms in a variety of simulated conditions, and compare the results to those given by traditional stochastic approaches which assume more information about the demands than is typically known. Our tests indicate that such online learning algorithms can perform well in comparison to stochastic approaches even when the stochastic approaches are given perfect information.