Decision making under uncertainty

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2011
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Li, Jian
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Deshpande, Amol
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Abstract
Almost all important decision problems are inevitably subject to some level of uncertainty either about data measurements, the parameters, or predictions describing future evolution. The significance of handling uncertainty is further amplified by the large volume of uncertain data automatically generated by modern data gathering or integration systems. Various types of problems of decision making under uncertainty have been subject to extensive research in computer science, economics and social science. In this dissertation, I study three major problems in this context, ranking, utility maximization, and matching, all involving uncertain datasets. First, we consider the problem of ranking and top-k query processing over probabilistic datasets. By illustrating the diverse and conflicting behaviors of the prior proposals, we contend that a single, specific ranking function may not suffice for probabilistic datasets. Instead we propose the notion of parameterized ranking functions, that generalize or can approximate many of the previously proposed ranking functions. We present novel exact or approximate algorithms for efficiently ranking large datasets according to these ranking functions, even if the datasets exhibit complex correlations or the probability distributions are continuous. The second problem concerns with the stochastic versions of a broad class of combinatorial optimization problems. We observe that the expected value is inadequate in capturing different types of risk-averse or risk-prone behaviors, and instead we consider a more general objective which is to maximize the expected utility of the solution for some given utility function. We present a polynomial time approximation algorithm with additive error ε for any ε > 0, under certain conditions. Our result generalizes and improves several prior results on stochastic shortest path, stochastic spanning tree, and stochastic knapsack. The third is the stochastic matching problem which finds interesting applications in online dating, kidney exchange and online ad assignment. In this problem, the existence of each edge is uncertain and can be only found out by probing the edge. The goal is to design a probing strategy to maximize the expected weight of the matching. We give linear programming based constant-factor approximation algorithms for weighted stochastic matching, which answer an open question raised in prior work.
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