With A.E.B. Lim and J.G. Shanthikumar

1. On the Optimality of Threshold Control in Robust Queues
We consider a single stage queuing system where arrivals and departures are modeled by point processes with stochastic intensities. An arrival incurs a cost while a departure earns a revenue. The objective is to maximize the profit by controlling the intensities subject to state dependent capacity limits and holding costs.  When arrival and departure processes are completely known, then a threshold policy is known to be optimal. Many times arrival and departure processes can not be accurately modeled and controlled due to lack of sufficient calibration data or inaccurate assumptions. We prove that a threshold policy is optimal under a max-min robust model when the uncertainty in the processes is characterized by relative entropy. Our model generalizes the standard notion of relative entropy to account for different levels of model uncertainty in arrival and departure processes. We also study the impact of the level of uncertainty on the optimal threshold level.

2. An Operational Learning Approach to Portfolio Optimization
We consider mean variance portfolio optimization problem. Classical approaches are known to perform poorly out of sample in the presence of estimation error. We introduce a new approach that guarantees a better out of sample performance than classical one. We explore the link between our approach and minimum norm portfolio. We reformulate the problem as a semidefinite program and show numerical results.


With A.E.B. Lim, J.G. Shanthikumar and L. Yu

3. Objective Operational Learning with Applications to Newsvendor Problem
It is well known that erroneous modeling can lead to severely suboptimal decisions if they are incorrect (e.g. the spiral down effect). We introduce a kernel based algorithm for combined learning and optimization that does not require strong assumptions about the relationship between order quantity and demand. We demonstrate promising empirical performance for small data sets under weak assumptions on the demand distribution.

4. Modeling Uncertainty and Flexible Modeling
Traditional models in manufacturing and services suffer from model and parametric uncertainty. In recent years much of the focus is on robust models that take into account modeling error. We study various robust modeling approaches and compare their performance out of sample and also in presence of modeling error. We also discuss new approaches to flexible modeling using operational learning.


With C.H. Xia and Z. Liu

5. Adaptive Resource Allocation for Multiple Correlated Hypotheses in Streaming Systems
Existing resource allocation schemes for query processing in a streaming environment fail to take into account (a) dependency between various sources of data (b) Probabilistic relationship between information retrieval rate and resource application rate (c) a dynamic way to split available resources among data streams to maximize information gain. A novel adaptive resource allocation mechanism is introduced where various hypotheses related to the query are identified and data streams are grouped with hypotheses. These hypotheses are related probabilistically and hence form a Bayesian (a specially layered one) network. A myopic resource allocation based on belief update equations and user’s utility function is used to split resources among hypotheses and subsequently among data streams.