SE PhD Prospectus Defense of Ruidi Chen

Title: Robust Predictive Procedures Using Robust Optimization

Abstract: We develop robust predictive methodologies using robust optimization within both stochastic and deterministic frameworks. The deterministic approach minimizes the maximum loss within an uncertainty set which contains all the possible values of the uncertain data. The uncertainty set is constructed based on the observed data and the risk preference of the decision maker. In the stochastic setting, we present a Distributionally Robust Optimization (DRO) approach to robust predictive analytics in a linear regression model, where the closeness of probability distributions is measured using the Wasserstein metric. Our Wasserstein DRO approach hedges against a family of distributions that are close to the empirical distribution. This distributional robustness enables accurate and stable estimate of the true regression plane in the presence of disturbances on the observed data. We show that the resulting formulation encompasses a class of models, which include the regularized Least Absolute Deviation (LAD), and the Grouped LASSO (GLASSO) as special cases. We build the connection between regularization and robustness through such a formulation. Two types of performance guarantees for the solution to our formulation are established under mild conditions. One is related to its out-of-sample prediction bias, and the other concerns the discrepancy between the estimated and true regression planes (estimation bias). Extensive numerical results demonstrate the superiority of our approach to other commonly used predictive procedures.

Committee: Advisor: Yannis Paschalidis, SE/ECE; Dimitris Bertsimas, MIT; David Castanon, SE/ECE; Venkatesh Saligrama, SE/ECE