Recently, there were multiple papers concerning distributionally robust optimization. They usually consider a single objective. In this talk, we generalize the concept into optimization problems with multiple objectives. We present several approaches based on scalarization, Pareto front and set comparison. We show the advantages and disadvantages of all approaches both from a theoretical point and computational complexity. We conclude the talk by a numerical comparison.
joint work with Duncan McElfresh, John P. Dickerson, Eric Rice
We consider the problem faced by a recommender system that seeks to offer a user their favorite item. Before making a recommendation, the system has the opportunity to elicit the user's preferences by making a moderate number of queries. We propose an exact robust optimization formulation of the problem which integrates the learning (preference elicitation) and recommendation phases and an equivalent reformulation as a mixed-binary linear program. We evaluate the performance of our approach on synthetic and real data from the US homeless youth where we learn the preferences of policy-makers.
joint work with David Simchi-Levi, Peter Yun Zhang
We study end-to-end design of a supply chain for antibiotics to defend against bioattacks. We model the defender’s inventory prepositioning and dispensing capacity installation decisions, attacker’s move, and defender’s adjustable shipment decisions, so as to minimize inventory and life loss costs, subject to population survivability targets. We provide theoretical backing to the performance of the Affinely Adjustable Robust Counterpart by proving its optimality under certain conditions. We conduct a high-fidelity case study with millions of nodes to guard against anthrax attacks in the US.