IE-OPIM Joint Graduate Seminar: Odysseas Kanavetas (Sabancı University)
“Asymptotically Optimal Multi-Armed Bandit Policies under Side Constraints and an Application on an Inventory Problem with Two Substitutable Products”
Date: Wednesday, March 9, 2016
Time: 13:40 – 14:30
Location: FENS L063
Abstract: We develop asymptotically optimal policies for the multi armed bandit (MAB) problem under side constraints. Such models are applicable in situations where each sample (or activation) from a population (bandit) incurs a known bandit dependent cost. We consider the class of feasible uniformly fast (f-UF) convergent policies, that satisfy sample path wise the cost constraint. We first establish a necessary asymptotic lower bound for the rate of increase of the regret function of f-UF policies. Then we construct a class of f-UF policies and provide conditions under which they are asymptotically optimal within the class of f-UF policies, achieving this asymptotic lower bound. As an application of adaptive policies we consider the problem of ordering for two products with stochastic demand and partial demand substitution. Successive demands arrive at random times, thus the order of arrivals affects the ending inventory and/or shortages. We have established the supermodularity of the expected cost function, which facilitates the computation of the optimal ordering policy. Finally, we consider extensions to the case of unknown parameters and suggest adaptive ordering policies.
Bio: Dr. Odysseas Kanavetas is currently a postdoctoral research fellow at department of Industrial Engineering, Sabancı University, Turkey. He received the B.Sc. degree in Mathematics (2005), the M.Sc. degree in Operations Research (2009) and Ph.D. degree in Operations Research (December, 2014) all of them from National and Kapodistrian University, Athens, Greece. His research interests lie in the areas of Operations Research and Stochastic Processes. In particular, his main interests concern optimization and adaptive learning aspects of stochastic systems with applications in queueing systems, healthcare management and supply chain management.