Distributionally Robust Optimization Techniques for Stochastic Optimal Control

Distributionally robust optimal control is a relatively new field of robust control that tries to address the issue of safety by hedging against the worst-cast distributions. However, because probability distributions are infinite-dimensional, this problem is in general computationally intractable. This thesis provides an overview of applications of distributionally robust optimization for stochastic optimal control. In particular, we look at existing and potentially new computationally tractable methods for performing distributionally robust optimal control using the Wasserstein metric.Undergraduat

Operational Decision Making under Uncertainty: Inferential, Sequential, and Adversarial Approaches

Modern security threats are characterized by a stochastic, dynamic, partially observable, and ambiguous operational environment. This dissertation addresses such complex security threats using operations research techniques for decision making under uncertainty in operations planning, analysis, and assessment. First, this research develops a new method for robust queue inference with partially observable, stochastic arrival and departure times, motivated by cybersecurity and terrorism applications. In the dynamic setting, this work develops a new variant of Markov decision processes and an algorithm for robust information collection in dynamic, partially observable and ambiguous environments, with an application to a cybersecurity detection problem. In the adversarial setting, this work presents a new application of counterfactual regret minimization and robust optimization to a multi-domain cyber and air defense problem in a partially observable environment