Thesis Title: Simulation Optimization in the Presence of Environmental Variables

Advisor:

Dr. Enlu Zhou, School of Industrial and Systems Engineering, Georgia Tech

Committee members: 

Dr. Seong-Hee Kim, School of Industrial and Systems Engineering, Georgia Tech

Dr. David Goldsman, School of Industrial and Systems Engineering, Georgia Tech

Dr. Siva Theja Maguluri, School of Industrial and Systems Engineering, Georgia Tech

Dr. Peter Frazier, Operations Research and Information Engineering, Cornell University

Date and Time: 8:00 am (EST), Tuesday, March 8th, 2022

Meeting URL:   https://bluejeans.com/281565731/8519

Meeting ID:  281 565 731 (BlueJeans)

Abstract: 

Systems whose performance can only be evaluated through expensive numerical or physical simulation are ubiquitous in practice. Numerous works that focus on optimization of such systems have been published over past decades. Simulation optimization refers to the study of finding the best system design where the system performance cannot be evaluated exactly and has to be estimated using a stochastic simulator. Depending on the problem setting, finding the best system design may entail selecting the alternative with the best performance among a finite set of alternatives or tuning a set of continuous parameters to find the best configuration. In many settings, there may be additional {\it environmental variables} present, which affect the performance of the system in various ways. By environmental variables, we refer to variables and conditions that affect the performance of implemented decision, that are beyond the control of the decision maker, and the value of which is unknown during optimization. As an example, the environmental variable can be the price sensitivities of the market participants, as in the two-sided market model in Chapter 2, or the unknown disease prevalence within the population, as in the COVID-19 testing allocation problem of Chapter 3.

In this thesis, we study several such problem settings, and propose methods for optimization of simulation-based systems in the presence of environmental variables.

In Chapter 2, we study a particular framework where the environmental variables denote the unknown input parameters of the simulator. We focus on the Bayesian Risk Optimization (BRO) framework, which imposes a Bayesian prior on the input parameters, and formulates a risk averse optimization problem for selecting a design while accounting for the uncertainty in the input parameters. We propose new stochastic gradient estimators for the nested risk measure objectives of BRO framework. We prove the consistency of the proposed estimators as well as the asymptotic convergence of the resulting stochastic approximation algorithms. We also present an empirical study demonstrating the effectiveness of the proposed algorithm.

In Chapter 3, we study a more general formulation of a simulation optimization problem with risk-aversion to the unknown environmental variable. In particular, we focus on optimization of a black-box, derivative-free, expensive to evaluate objective whose performance depends on an environmental variable which is only revealed after the selected design is implemented. We assume that the objective can be simulated for any given design - environmental variable pair, and focus on optimizing a risk measure of the objective calculated over the probability distribution of the environmental variable. We use a Gaussian process surrogate model to approximate the response surface, and propose a highly sample efficient Bayesian optimization approach. We demonstrate the superior sampling efficiency of our approach in numerical experiments.

In Chapter 4, we deviate from the risk-averse formulations studied in the earlier chapters and instead focus on a setting where the final decision is made after observing the environmental variable. We again consider a setting where the solution performance is affected by the environmental variable. We suppose that the experimentation is costly and that the decision has to be made swiftly once the environmental variable is revealed. Thus, our goal is to identify a mapping from the space of environmental variables to the space of alternative designs, which is to be used to select the best design once the environmental variable is observed. We propose a new sequential sampling policy that uses a Gaussian process surrogate model of the response surface. Our sampling policy is based on a large deviations analysis of the probability of correctly selecting the best alternative, comes with strong asymptotic performance guarantees, and demonstrates high sampling efficiency and low computational cost in numerical experiments.