Model Uncertainty, Robust Optimization and Learning

Classical modelling approaches in OR/MS under uncertainty assume a full probabilis- tic characterization. The learning needed to implement the policies derived from these models is accomplished either through (i) classical statistical estimation procedures or (ii) subjective Bayesian priors. When the data available for learning is limited, or the underlying uncertainty is non-stationary, the error induced by these approaches can be significant and the effectiveness of the policies derived will be reduced. In this tutorial we discuss how we may incorporate these errors in the model (that is, model model uncertainty) and use robust optimization to derive efficient policies. Different models of model uncertainty will be discussed and different approaches to robust opti- mization with and without bench-marking will be presented. Two alternative learning approaches Objective Bayesian Learning and Operational Learning will be discussed. These approaches could be used to calibrate the models of model uncertainty and to calibrate the optimal policies. Throughout this tutorial we will consider the classical inventory control problem, the inventory control problem with censored demand data and the portfolio selection problem as examples to illustrate these ideas.