Year of Publication

2016

Degree Name

Doctor of Philosophy (PhD)

Document Type

Doctoral Dissertation

College

Engineering

Department

Computer Science

First Advisor

Dr. Miroslaw Truszczynski

Abstract

Preferences are fundamental to decision making and play an important role in artificial intelligence. Our research focuses on three group of problems based on the preference formalism Answer Set Optimization (ASO): preference aggregation problems such as computing optimal (near optimal) solutions, strategic behaviors in preference representation, and learning ranks (weights) for preferences.

In the first group of problems, of interest are optimal outcomes, that is, outcomes that are optimal with respect to the preorder defined by the preference rules. In this work, we consider computational problems concerning optimal outcomes. We propose, implement and study methods to compute an optimal outcome; to compute another optimal outcome once the first one is found; to compute an optimal outcome that is similar to (or, dissimilar from) a given candidate outcome; and to compute a set of optimal answer sets each significantly different from the others. For the decision version of several of these problems we establish their computational complexity.

For the second topic, the strategic behaviors such as manipulation and bribery have received much attention from the social choice community. We study these concepts for preference formalisms that identify a set of optimal outcomes rather than a single winning outcome, the case common to social choice. Such preference formalisms are of interest in the context of combinatorial domains, where preference representations are only approximations to true preferences, and seeking a single optimal outcome runs a risk of missing the one which is optimal with respect to the actual preferences. In this work, we assume that preferences may be ranked (differ in importance), and we use the Pareto principle adjusted to the case of ranked preferences as the preference aggregation rule. For two important classes of preferences, representing the extreme ends of the spectrum, we provide characterizations of situations when manipulation and bribery is possible, and establish the complexity of the problem to decide that.

Finally, we study the problem of learning the importance of individual preferences in preference profiles aggregated by the ranked Pareto rule or positional scoring rules. We provide a polynomial-time algorithm that finds a ranking of preferences such that the ranked profile correctly decided all the examples, whenever such a ranking exists. We also show that the problem to learn a ranking maximizing the number of correctly decided examples is NP-hard. We obtain similar results for the case of weighted profiles.

Digital Object Identifier (DOI)

http://dx.doi.org/10.13023/ETD.2016.197

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