Probability and Optimization: A Beautiful Combination

The composition of data proliferation, advances in statistical learning methods, and growth in computational power creates tremendous opportunities for addressing the ever-present uncertainty and risks in real-world problems from a mathematical perspective.  We consider a general approach that provides a mathematical foundation for general classes of stochastic models and optimal decision making within the context of these stochastic models.  A couple of representative examples will be discussed to illustrate instances of our general approach.  This includes one case in which we formulate a stochastic model of a fundamental dynamic resource allocation problem and derive an optimal control policy within the model that renders efficient algorithms to govern resource allocations over time; and another case in which we revisit a classical multidimensional Erlang loss model for which we derive fundamental properties of both the stochastic model and optimal decisions within the model, as well as further investigating new mathematical approximations of probability measures of interest.  This research is based on joint works with X. Gao, Y. Lu, M. Sharma, J.W. Bosman and K. Jung, Y. Lu, D. Shah, M. Sharma.