Theses and Dissertations from UMD
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New submissions to the thesis/dissertation collections are added automatically as they are received from the Graduate School. Currently, the Graduate School deposits all theses and dissertations from a given semester after the official graduation date. This means that there may be up to a 4 month delay in the appearance of a give thesis/dissertation in DRUM
More information is available at Theses and Dissertations at University of Maryland Libraries.
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Item Decision Making Under Uncertainty: New Models and Applications(2018) Jie, Cheng; Fu, Michael C; Applied Mathematics and Scientific Computation; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)In the settings of decision-making-under-uncertainty problems, an agent takes an action on the environment and obtains a non-deterministic outcome. Such problem settings arise in various applied research fields such as financial engineering, business analytics and speech recognition. The goal of the research is to design an automated algorithm for an agent to follow in order to find an optimal action according to his/her preferences.Typically, the criterion for selecting an optimal action/policy is a performance measure, determined jointly by the agent's preference and the random mechanism of the agent's surrounding environment. The random mechanism is reflected through a random variable of the outcomes attained by a given action, and the agent's preference is captured by a transformation on the potential outcomes from the set of possible actions. Many decision-making-under-uncertainty problems formulate the performance measure objective function and develop optimization schemes on that objective function. Although the idea on the high-level seems straightforward, there are many challenges, both conceptually and computationally, that arise in the process of finding the optimal action. The thesis studies a special class of performance measure defined based on Cumulative Prospect Theory (CPT), which has been used as an alternative to expected-utility based performance measure for evaluating human-centric systems. The first part of the thesis designs a simulation-based optimization framework on the CPT-based performance measure. The framework includes a sample-based estimator for the CPT-value and stochastic approximation algorithms for searching the optimal action/policy. We prove that, under reasonable assumptions, the CPT-value estimator is asymptotically consistent and our optimization algorithms are asymptotically converging to the optimal point. The second part of the thesis introduces an abstract dynamic programming framework whose transitional measure is defined through the CPT-value. We also provide sufficient conditions under which the CPT-driven dynamic programming would attain a unique optimal solution. Empirical experiments presented in the last part of thesis illustrate that the CPT-estimator is consistent and that the CPT-based performance measure may lead to an optimal policy very different from those obtained using traditional expected utility.Item Stochastic Systems with Cumulative Prospect Theory(2013) Lin, Kun; Marcus, Steven I.; Electrical Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Stochastic control problems arise in many fields. Traditionally, the most widely used class of performance criteria in stochastic control problems is risk-neutral. More recent attempts at introducing risk-sensitivity into stochastic control problems include the application of utility functions. The decision theory community has long debated the merits of using expected utility for modeling human behaviors, as exemplified by the Allais paradox. Substantiated by strong experimental evidence, Cumulative Prospect Theory (CPT) based performance measures have been proposed as alternatives to expected utility based performance measures for evaluating human-centric systems. Our goal is to study stochastic control problems using performance measures derived from the cumulative prospect theory. The first part of this thesis solves the problem of evaluating Markov decision processes (MDPs) using CPT-based performance measures. A well-known method of solving MDPs is dynamic programming, which has traditionally been applied with an expected utility criterion. When the performance measure is CPT-inspired, several complications arise. Firstly, when solving a problem via dynamic programming, it is important that the performance criterion has a recursive structure, which is not true for all CPT-based criteria. Secondly, we need to prove the traditional optimality criteria for the updated problems (i.e., MDPs with CPT-based performance criteria). The theorems stated in this part of the thesis answer the question: what are the conditions required on a CPT-inspired criterion such that the corresponding MDP is solvable via dynamic programming? The second part of this thesis deals with stochastic global optimization problems. Using ideas from the cumulative prospect theory, we are able to introduce a novel model-based randomized optimization algorithm: Cumulative Weighting Optimization (CWO). The key contributions of our research are: 1) proving the convergence of the algorithm to an optimal solution given a mild assumption on the initial condition; 2) showing that the well-known cross-entropy optimization algorithm is a special case of CWO-based algorithms. To the best knowledge of the author, there is no previous convergence proof for the cross-entropy method. In practice, numerical experiments have demonstrated that a CWO-based algorithm can find a better solution than the cross-entropy method. Finally, in the future, we would like to apply some of the ideas from cumulative prospect theory to games. In this thesis, we present a numerical example where cumulative prospect theory has an unexpected effect on the equilibrium points of the classic prisoner's dilemma game.