Robust solution schemes for queue management, fair classification and portfolio selection
Creators: name: Wang, Yijie (Ph. D. In Operations Research And Industrial Engineering)
Publisher: name: The University of Texas at Austin
Year: 2023
Subjects: Robust optimization
Queue theory
Fair classification
Portfolio selection

description: This dissertation broadly focuses on designing robust solution schemes for decision making problems under uncertainty. Specifically, we consider important problems in three domains: queue management, fair classification, and portfolio management. We deliver novel models and reformulations for the three problems while offering insightful theoretical understandings and statistical performance guarantees. In the first part of the dissertation, we present an extension of Naor’s analysis on the join-or-balk problem in observable M/M/1 queues. While all other Markovian assumptions still hold, we explore this problem assuming uncertain arrival rates under the distributionally robust settings. We first study the problem with the classical moment ambiguity set, where the support, mean, and mean-absolute deviation of the underlying distribution are known. Next, we extend the model to the data-driven setting, where decision makers only have access to a finite set of samples. We develop three optimal joining threshold strategies from the perspective of an individual customer, a social optimizer, and a revenue maximizer, such that their respective worst-case expected benefit rates are maximized. Finally, we compare our findings with Naor’s original results and the traditional sample average approximation scheme. The second part of the dissertation proposes a distributionally robust classification model with a fairness constraint that encourages the classifier to be fair in view of the equality of opportunity criterion. We use a type-∞ Wasserstein ambiguity set centered at the empirical distribution to model distributional uncertainty and derive a conservative reformulation for the worst-case equal opportunity unfairness measure. We establish that the model is equivalent to a mixed binary optimization problem, which can be solved by standard off-the-shelf solvers. To improve scalability, we further propose a convex, hinge-loss-based model for large problem instances whose reformulation does not incur any binary variables. Moreover, we also consider the distributionally robust learning problem with a generic ground transportation cost to hedge against the uncertainties in the label and sensitive attribute. Finally, we numerically demonstrate that our proposed approaches improve fairness with negligible loss of predictive accuracy. Our study raises awareness that bias may arise when predictive models are employed in service and operations. It generally comes from human bias, e.g., unbalanced data collection or low sample sizes, and gets further amplified by algorithms. Incorporating fairness constraints along with the distributionally robust optimization (DRO) scheme is a powerful way to alleviate algorithmic bias. In the last part of the dissertation, we study the portfolio optimization problem with contextual information that is available to better quantify and predict the uncertain returns of assets. Motivated by the regime modeling techniques for the finance market, we consider the setting where both the uncertain returns and the contextual information follow a Gaussian Mixture (GM) distribution. This problem is shown to be equivalent to a nominal portfolio optimization problem where the means and the covariance matrix are adjusted by the contextual information. We then apply robust optimization and propose the robust contextual portfolio optimization problem, which reduces the sensitivity of model parameters used in the Gaussian Mixture Model (GMM). A tractable formulation is derived to approximate the solution of the robust contextual portfolio optimization problem. We conduct a numerical experiment in the US equity markets, and the results demonstrate the advantage of our proposed model against other benchmark methods.