joint work with Andreas Bärmann, Alexander Martin, O. Schneider
Robust optimization can be solved via online learning requiring only access to the nominal problem for a given uncertainty realization. We show that a similar perspective can be assumed for an online learning approach to online inverse optimization, even for discrete and non-convex decisions. The decision maker observes an expert's decisions over time and learns an objective function that is equivalent to the expert's private objective. We present a new framework for inverse optimization through online learning that goes beyond duality approaches and demonstrate its real-world applicability.
joint work with Omid Nohadani, Chaithanya Bandi
We introduce a new class of adaptive policies called periodic-affine policies, that allows a decision maker to optimally manage and control large-scale newsvendor networks in the presence of uncertain demand without distributional assumptions. These policies model many features of the demand such as correlation, and can be generalized to multi-product settings and multi-period problems. This is accomplished by modeling the uncertain demand via sets. We provide efficient algorithms and demonstrate their advantages on the sales data from one of India’s largest pharmacy retailers.
joint work with Nikos Trichakis, Do-Young Yoon
We consider a system with an evolving state that can be stopped at any time by a decision maker (DM), yielding a state-dependent reward. The DM observes the state only at limited number of monitoring times, which he must choose, in conjunction with a stopping policy. We propose a robust optimization approach, whereby adaptive uncertainty sets capture the information acquired through monitoring. We consider two versions of the problem, static and dynamic and show that, under certain conditions, the same reward is achievable under either static or dynamic monitoring.