Industrial Engineering Seminar Series - Burak Kocuk

Title: Computational Aspects of Bayesian Solution Estimators in Stochastic Optimization

Abstract: We study a class of stochastic programs where some of the elements in the objective function are random, and their probability distribution has unknown parameters. The goal is to find a good estimate for the optimal solution of the stochastic program using data sampled from the distribution of the random elements. We investigate two common optimization criteria for evaluating the quality of a solution estimator, one based on the difference in objective values, and the other based on the Euclidean distance between solutions. We use risk as the expected value of such criteria over the sample space. Under a Bayesian framework, where a prior distribution is assumed for the unknown parameters, two natural estimation-optimization strategies arise. A separate scheme first finds an estimator for the unknown parameters, and then uses this estimator in the optimization problem. A joint scheme combines the estimation and optimization steps by directly adjusting the distribution in the stochastic program. We analyze the risk difference between the solutions obtained from these two schemes for several classes of stochastic programs, while providing insight on the computational effort to solve these problems. (Joint work with Danial Davarnia and Gérard Cornuéjols)

Bio: Burak Kocuk is an Assistant Professor at the Industrial Engineering Program, Sabancı University. He obtained his BS degrees in Industrial Engineering and Mathematics, and MS degree in Industrial Engineering from Boğaziçi University. He obtained his PhD degree of Operations Research at the School of Industrial and Systems Engineering, Georgia Institute of Technology. Before joining Sabancı University, he was a postdoctoral fellow at the Tepper School of Business, Carnegie Mellon University. His current research focuses on mixed-integer nonlinear programming problems, from both theoretical and methodological aspects.