Robust Optimization and Learning Under Uncertainty
By Aida Rahmattalabi
Decision making in an uncertain world is a challenging problem both from modeling and optimization perspectives. In the session “Robust Optimization and Learning under Uncertainty,” some of these problems were discussed. The first talk was given by Han Yu, PhD student at the University of Southern California. In her talk, she introduced an important, yet relatively underexplored problem: a lot of real-world decision-making problems happen over time, where an individual makes decisions, obtains information, and using this history, makes additional decisions in the future. But, what if the information that we receive is also impacted by the decisions we make in the first place? These problems, as you can expect, quickly become intractable. In her talk, Han Yu introduced an efficient approach of solving this class of problems.
In a subsequent talk, Phebe Vayanos, Assistant Professor at the University of Southern California, introduced a novel application of decision-dependent information discovery in the context of policy design. Suppose you are in a room with policymakers or stakeholders asking you to design an optimal policy. However, they have many objectives: namely, fairness, efficiency, and interpretability of the policy. In this scenario, and without knowing the precise preferences of the policymakers, how can one propose a satisfactory policy? The first step is to learn the preferences in order to inform the policymaking problem downstream. In her talk, Phebe Vayanos shared how one can use techniques from robust optimization to tackle this problem.
The final talk of the session targeted the multi-armed bandit problem under adversarial attacks. These problems arise when one needs to make a decision, whose utility is uncertain. The goal is to find a policy that maximizes the total utility while trading off between learning the good action, by exploration, and exploiting the current knowledge, via exploitation. In many real-world applications, and when there is the possibility of adversarial attacks, existing approaches fail to provide reasonable policies. The last talk proposed a novel extension of distributionally robust optimization to address this problem.