Euclidean preferences are a widely studied preference model, in which decision makers and alternatives are embedded in d-dimensional Euclidean space. Decision makers prefer those alternatives closer to them. This model, also known as multidimensional unfolding, has applications in economics, psychometrics, marketing, and many other fields. We study the problem of deciding whether a given preference profile is d -Euclidean. For the one-dimensional case, polynomial-time algorithms are known. We show that, in contrast, for every other fixed dimension d > 1, the recognition problem is equivalent to the existential theory of the reals (ETR), and so in particular NP-hard. We further show that some Euclidean preference profiles require exponentially many bits in order to specify any Euclidean embedding, and prove that the domain of d-Euclidean preferences does not admit a finite forbidden minor characterisation for any d > 1. We also study dichotomous preferences and the behaviour of other metrics, and survey a variety of related work.

Security problems can be modeled as two-player partially observable stochastic games with one-sided partial observability and infinite horizon (one-sided POSGs). We seek for optimal strategies of player 1 that correspond to robust strategies against the worst-case opponent (player 2) that is assumed to have a perfect information about the game. We present a novel algorithm for approximately solving one-sided POSGs based on the heuristic search value iteration (HSVI) for POMDPs. Our results include (1) theoretical properties of one-sided POSGs and their value functions, (2) guarantees showing the convergence of our algorithm to optimal strategies, and (3) practical demonstration of applicability and scalability of our algorithm on three different domains: pursuit-evasion, patrolling, and search games.

We demonstrate an integrated system for building and learning models and structures in both a real and virtual environment. The system combines natural language understanding, planning, and methods for composition of basic concepts into more complicated concepts. The user and the system interact via natural language to jointly plan and execute tasks involving building structures, with clarifications and demonstrations to teach the system along the way. We use the same architecture for building and simulating models of biology, demonstrating the general-purpose nature of the system where domain-specific knowledge is concentrated in sub-modules with the basic interaction remaining domain-independent. These capabilities are supported by our work on semantic parsing, which generates knowledge structures to be grounded in a physical representation, and composed with existing knowledge to create a dynamic plan for completing goals. Prior work on learning from natural language demonstrations enables learning of models from very few demonstrations, and features are extracted from definitions in natural language. We believe this architecture for interaction opens up a wide possibility of human-computer interaction and knowledge transfer through natural language.

The Minimum Sum Coloring Problem (MSCP) is an NP-Hard problem derived from the graph coloring problem (GCP) and has practical applications in different domains such as VLSI design, distributed resource allocation, and scheduling. There exist few exact solutions for MSCP, probably due to its search space much more elusive than that of GCP. On the contrary, much effort is spent in the literature to develop upper and lower bounds for MSCP. In this paper, we borrow a notion called motif, that was used in a recent work for upper bounding the minimum number of colors in an optimal solution of MSCP, to develop a new algebraic lower bound called for MSCP. Experiments on standard benchmarks for MSCP and GCP show that this new lower bound is substantially better than the existing lower bounds for several families of graphs.

Systems deployed in unstructured environments must be able to adapt to novel situations. This requires the ability to perform in domains that may be vastly different from training domains. My dissertation focuses on the representations used in lifelong learning and how these representations enable predictions and knowledge sharing over time, allowing an agent to continuously learn and adapt in changing environments. Specifically, my contributions will enable lifelong learning systems to efficiently accumulate data, use prior knowledge to predict models for novel tasks, and alter existing models to account for changes in the environment.

Axioms can be used to model derived predicates in domain-independent planning models. Formulating models which use axioms can sometimes result in problems with much smaller search spaces than the original model. We propose a method for automatically extracting a particular class of axioms from standard STRIPS PDDL models. More specifically, we identify operators whose effects become irrelevant given some other operator, and generate axioms that capture this relationship. We show that this algorithm can be used to successfully extract axioms from standard IPC benchmark instances, and show that the extracted axioms can be used to significantly improve the performance of an IP-based planner.

Bounding the partition function is a key inference task in many graphical models. In this paper, we develop an anytime anyspace search algorithm taking advantage of AND/OR tree structure and optimized variational heuristics to tighten deterministic bounds on the partition function. We study how our priority-driven best-first search scheme can improve on state-of-the-art variational bounds in an anytime way within limited memory resources, as well as the effect of the AND/OR framework to exploit conditional independence structure within the search process within the context of summation. We compare our resulting bounds to a number of existing methods, and show that our approach offers a number of advantages on real-world problem instances taken from recent UAI competitions.

Atrial fibrillation (AF), the most common arrhythmia with clinical significance, is a serious public health problem. Yet a number of studies show that current AF management is suboptimal due to a knowledge gap between primary care physicians and evidence-based treatment recommendations. This gap is caused by a number of barriers such as a lack of knowledge about new therapies, challenges associated with multi-morbidity, or a lack of patient engagement in therapy planning. The decision support tools proposed to address these barriers handle individual barriers but none of them tackle them comprehensively. Responding to this challenge, we propose AFGuide -- a clinical decision support system to educate and support primary care physicians in developing evidence-based and optimal AF therapies that take into account multi-morbid conditions and patient preferences. AFGuide relies on artificial intelligence techniques (logical reasoning) and preference modeling techniques, and combines them with mobile computing technologies. In this paper we present the design of the system and discuss its proposed implementation and evaluation.

Symmetry-breaking is a technique for efficiently solving SAT instances that contain high degrees of symmetry among the variables of the instance. When satisfiability problems are represented as a relational schema, symmetries between objects in the domain can be detected directly from evidence, that is, variables known to have a particular setting prior to solving. These symmetries between domain objects are called term symmetries. In this work, we present two novel extensions to the technique of term equivalent symmetry breaking which allow the detection and exploitation of conditional or hidden symmetries, those relationships between domain objects that are obscured until the instance is partially solved. We give promising preliminary experimental results for this technique, and discuss how the techniques could be extended for use in probabilistic domains.

Extensive-form games with imperfect recall are an important model of dynamic games where the players forget previously known information. Often, imperfect recall games are the result of an abstraction algorithm that simplifies a large game with perfect recall. Unfortunately, solving an imperfect recall game has fundamental problems since a Nash equilibrium does not have to exist. Alternatively, we can seek maxmin strategies that guarantee an expected outcome. The only existing algorithm computing maxmin strategies in imperfect recall games, however, requires approximating a bilinear program that is proportional to the size of the game and thus has a limited scalability. We propose a novel algorithm for computing maxmin strategies that combines this approximate algorithm with an incremental strategy-generation technique designed previously for extensive-form games with perfect recall. Experimental evaluation shows that the novel algorithm builds only a fraction of the game tree and improves the scalability by several orders of magnitude. Finally, we demonstrate that our algorithm can solve an abstracted variant of a large game faster compared to the algorithms operating on the unabstracted perfect-recall variant.