Tuesday, Dec 4 | 11 a.m. | BYENG MI-09
The efficacy of robust optimization under uncertainty spans a variety of settings with complex risk requirements. The growing data size and increasing intricacy of risk measures demand more versatile and efficient algorithms that accommodate richer characterizations of uncertainty. In this talk, I present my recent research on uncovering and leveraging problem structures that reveal deeper insights and allows for more capable methods. In the first part, I discuss how capturing decision- dependent structures in uncertainties improves solutions for real-world challenges. We provide a new class of uncertainty sets that allows tractable reformulations. Decision makers can then expend resources for gathering information or improving conditions before committing to a decision. This proactive uncertainty control mitigates the over-conservatism of current approaches. In the second part, I discuss how harnessing the inherent temporal structure (e.g., sub-periodicity) in multiperiod dynamic systems allows us to optimally solve large-scale dynamic programs efficiently. We introduce a new class of adaptive policies called periodic-affine policies, for managing large-scale newsvendor networks under demand uncertainty. These policies are data-driven and can model correlation for example. We then generalize the model to multi-product settings and multi-period problems and show that these policies are sustainable, i.e., time consistent. This approach is tractable and free of distributional assumptions, hence, suited for real-world applications. To demonstrate the performance in each part, a routing and a healthcare application will be discussed.