Various tasks in decision making and decision support systems require selecting a preferred subset of a given set of items. Here we focus on problems where the individual items are described using a set of characterizing attributes, and a generic preference specification is required, that is, a specification that can work with an arbitrary set of items. For example, preferences over the content of an online newspaper should have this form: At each viewing, the newspaper contains a subset of the set of articles currently available. Our preference specification over this subset should be provided offline, but we should be able to use it to select a subset of any currently available set of articles, e.g., based on their tags. We present a general approach for lifting formalisms for specifying preferences over objects with multiple attributes into ones that specify preferences over subsets of such objects. We also show how we can compute an optimal subset given such a specification in a relatively efficient manner. We provide an empirical evaluation of the approach as well as some worst-case complexity results.

Informally, a set of abstractions of a state space S is additive if the distance between any two states in S is always greater than or equal to the sum of the corresponding distances in the abstract spaces. The first known additive abstractions, called disjoint pattern databases, were experimentally demonstrated to produce state of the art performance on certain state spaces. However, previous applications were restricted to state spaces with special properties, which precludes disjoint pattern databases from being defined for several commonly used testbeds, such as Rubik's Cube, TopSpin and the Pancake puzzle. In this paper we give a general definition of additive abstractions that can be applied to any state space and prove that heuristics based on additive abstractions are consistent as well as admissible. We use this new definition to create additive abstractions for these testbeds and show experimentally that well chosen additive abstractions can reduce search time substantially for the (18,4)-TopSpin puzzle and by three orders of magnitude over state of the art methods for the 17-Pancake puzzle. We also derive a way of testing if the heuristic value returned by additive abstractions is provably too low and show that the use of this test can reduce search time for the 15-puzzle and TopSpin by roughly a factor of two.

Real-time heuristic search is a challenging type of agent-centered search because the agent's planning time per action is bounded by a constant independent of problem size. A common problem that imposes such restrictions is pathfinding in modern computer games where a large number of units must plan their paths simultaneously over large maps. Common search algorithms (e.g., A*, IDA*, D*, ARA*, AD*) are inherently not real-time and may lose completeness when a constant bound is imposed on per-action planning time. Real-time search algorithms retain completeness but frequently produce unacceptably suboptimal solutions. In this paper, we extend classic and modern real-time search algorithms with an automated mechanism for dynamic depth and subgoal selection. The new algorithms remain real-time and complete. On large computer game maps, they find paths within 7% of optimal while on average expanding roughly a single state per action. This is nearly a three-fold improvement in suboptimality over the existing state-of-the-art algorithms and, at the same time, a 15-fold improvement in the amount of planning per action.

Multi-agent planning in stochastic environments can be framed formally as a decentralized Markov decision problem. Many real-life distributed problems that arise in manufacturing, multi-robot coordination and information gathering scenarios can be formalized using this framework. However, finding the optimal solution in the general case is hard, limiting the applicability of recently developed algorithms. This paper provides a practical approach for solving decentralized control problems when communication among the decision makers is possible, but costly. We develop the notion of communication-based mechanism that allows us to decompose a decentralized MDP into multiple single-agent problems. In this framework, referred to as decentralized semi-Markov decision process with direct communication (Dec-SMDP-Com), agents operate separately between communications. We show that finding an optimal mechanism is equivalent to solving optimally a Dec-SMDP-Com. We also provide a heuristic search algorithm that converges on the optimal decomposition. Restricting the decomposition to some specific types of local behaviors reduces significantly the complexity of planning. In particular, we present a polynomial-time algorithm for the case in which individual agents perform goal-oriented behaviors between communications. The paper concludes with an additional tractable algorithm that enables the introduction of human knowledge, thereby reducing the overall problem to finding the best time to communicate. Empirical results show that these approaches provide good approximate solutions.

Sentence compression holds promise for many applications ranging from summarization to subtitle generation. Our work views sentence compression as an optimization problem and uses integer linear programming (ILP) to infer globally optimal compressions in the presence of linguistically motivated constraints. We show how previous formulations of sentence compression can be recast as ILPs and extend these models with novel global constraints. Experimental results on written and spoken texts demonstrate improvements over state-of-the-art models.

Entity resolution is the problem of reconciling database references corresponding to the same real-world entities. Given the abundance of publicly available databases that have unresolved entities, we motivate the problem of query-time entity resolution quick and accurate resolution for answering queries over such `unclean' databases at query-time. Since collective entity resolution approaches --- where related references are resolved jointly --- have been shown to be more accurate than independent attribute-based resolution for off-line entity resolution, we focus on developing new algorithms for collective resolution for answering entity resolution queries at query-time. For this purpose, we first formally show that, for collective resolution, precision and recall for individual entities follow a geometric progression as neighbors at increasing distances are considered. Unfolding this progression leads naturally to a two stage `expand and resolve' query processing strategy. In this strategy, we first extract the related records for a query using two novel expansion operators, and then resolve the extracted records collectively. We then show how the same strategy can be adapted for query-time entity resolution by identifying and resolving only those database references that are the most helpful for processing the query. We validate our approach on two large real-world publication databases where we show the usefulness of collective resolution and at the same time demonstrate the need for adaptive strategies for query processing. We then show how the same queries can be answered in real-time using our adaptive approach while preserving the gains of collective resolution. In addition to experiments on real datasets, we use synthetically generated data to empirically demonstrate the validity of the performance trends predicted by our analysis of collective entity resolution over a wide range of structural characteristics in the data.

A pattern database (PDB) is a heuristic function implemented as a lookup table that stores the lengths of optimal solutions for subproblem instances. Standard PDBs have a distinct entry in the table for each subproblem instance. In this paper we investigate compressing PDBs by merging several entries into one, thereby allowing the use of PDBs that exceed available memory in their uncompressed form. We introduce a number of methods for determining which entries to merge and discuss their relative merits. These vary from domain-independent approaches that allow any set of entries in the PDB to be merged, to more intelligent methods that take into account the structure of the problem. The choice of the best compression method is based on domain-dependent attributes. We present experimental results on a number of combinatorial problems, including the four-peg Towers of Hanoi problem, the sliding-tile puzzles, and the Top-Spin puzzle. For the Towers of Hanoi, we show that the search time can be reduced by up to three orders of magnitude by using compressed PDBs compared to uncompressed PDBs of the same size. More modest improvements were observed for the other domains.

Real-time heuristic search methods are used by situated agents in applications that require the amount of planning per move to be independent of the problem size. Such agents plan only a few actions at a time in a local search space and avoid getting trapped in local minima by improving their heuristic function over time. We extend a wide class of real-time search algorithms with automatically-built state abstraction and prove completeness and convergence of the resulting family of algorithms. We then analyze the impact of abstraction in an extensive empirical study in real-time pathfinding. Abstraction is found to improve efficiency by providing better trading offs between planning time, learning speed and other negatively correlated performance measures.

In this paper, we study the possibility of designing non-trivial random CSP models by exploiting the intrinsic connection between structures and typical-case hardness. We show that constraint consistency, a notion that has been developed to improve the efficiency of CSP algorithms, is in fact the key to the design of random CSP models that have interesting phase transition behavior and guaranteed exponential resolution complexity without putting much restriction on the parameter of constraint tightness or the domain size of the problem. We propose a very flexible framework for constructing problem instances with interesting behavior and develop a variety of concrete methods to construct specific random CSP models that enforce different levels of constraint consistency. A series of experimental studies with interesting observations are carried out to illustrate the effectiveness of introducing structural elements in random instances, to verify the robustness of our proposal, and to investigate features of some specific models based on our framework that are highly related to the behavior of backtracking search algorithms.

We introduce a new algorithm for off-policy temporal-difference learning with function approximation that has lower variance and requires less knowledge of the behavior policy than prior methods. We develop the notion of a recognizer, a filter on actions that distorts the behavior policy to produce a related target policy with low-variance importance-sampling corrections. We also consider target policies that are deviations from the state distribution of the behavior policy, such as potential temporally abstract options, which further reduces variance. This paper introduces recognizers and their potential advantages, then develops a full algorithm for linear function approximation and proves that its updates are in the same direction as on-policy TD updates, which implies asymptotic convergence. Even though our algorithm is based on importance sampling, we prove that it requires absolutely no knowledge of the behavior policy for the case of state-aggregation function approximators.