The method of types is one of the key technical tools in Information Theory with applications to Shannon theory, hypothesis testing and large deviations theory. In this talk, we present results using this approach to construct generalized typical sets that allow us analyze and optimize the expected behavior of stochastic systems. We then use the idea of Averaged RO approach developed by Bertsimas and Youssef (2019) to approximate and optimize the expected behavior. We illustrate our approach by finding optimal control policies for multi-class queueing networks arising in data centers.
joint work with Jin Qi, Aiqi Zhang
We solve a class of two-stage distributionally robust optimization problems which are with the property of supermodular. We apply the monotone coupling results and derive the worst-case distribution precisely, which leads to the tractability of this two-stage distributionally robust optimization problem. Furthermore, we provide a necessary and sufficient condition to check if any given problem has supermodular property. We apply this framework to classical problems including multi-item newsvendor problems, general assemble-to-order (ATO) systems and the appointment scheduling problem.
joint work with Omar El Housni
Affine policies are widely used in dynamic optimization where computing an optimal adjustable solution is often intractable. While the worst case performance of affine policies is significantly bad, the observed empirical performance is near-optimal for a large class of instances. In this paper, we aim to address this stark-contrast between the worst-case and the empirical performance of affine policies, and show that affine policies give a provably good approximation for two-stage robust optimization problem with high probability on random instances for a large class of distributions.