Clearing the Jungle of Stochastic Optimization

Abstract

Whereas deterministic optimization enjoys an almost universally accepted canonical form, stochastic optimization is a jungle of competing notational systems and algorithmic strategies. This is especially problematic in the context of sequential (multistage) stochastic optimization problems, which is the focus of our presentation. In this article, we place a variety of competing strategies into a common framework, which makes it easier to see the close relationship between communities such as stochastic programming, (approximate) dynamic programming, simulation, and stochastic search. What have previously been viewed as competing approaches (e.g., simulation versus optimization, stochastic programming versus dynamic programming) can be reduced to four fundamental classes of policies that are evaluated in a simulation-based setting we call the base model. The result is a single coherent framework that encompasses all of these methods, which can often be combined to create powerful hybrid policies to address complex problems.