Here \unlikely" means \unless some complexity classes collapse," where the collapses considered are P NP, P PSPACE, or P EXP. Until or unless these collapses are shown to hold, any control-policy designer must choose between such performance guarantees and ecient computation. In this work, we show that uncertainty breeds uncertainty: In a controlled stochastic system with uncertainty (as modeled by a partially observable Markov decision process, for example), plans can be obtained eciently or with quality guarantees, but rarely both. Planning over stochastic domains with uncertainty is hard (in some cases PSPACEhard or even undecidable, see Papadimitriou & Tsitsiklis, 1987; Madani, Hanks, & Condon, 1999). Given that it is hard to nd an optimal plan or policy, it is natural to try to nd one that is \good enough". In the best of all possible worlds, this would mean having an algorithm that is guaranteed to be fast and to produce a policy that is reasonably close to the optimal policy.

Functional relationships between objects, called `attributes', are of considerable importance in knowledge representation languages, including Description Logics (DLs). A study of the literature indicates that papers have made, often implicitly, different assumptions about the nature of attributes: whether they are always required to have a value, or whether they can be partial functions. The work presented here is the first explicit study of this difference for subclasses of the CLASSIC DL, involving the same-as concept constructor. It is shown that although determining subsumption between concept descriptions has the same complexity (though requiring different algorithms), the story is different in the case of determining the least common subsumer (lcs). For attributes interpreted as partial functions, the lcs exists and can be computed relatively easily; even in this case our results correct and extend three previous papers about the lcs of DLs. In the case where attributes must have a value, the lcs may not exist, and even if it exists it may be of exponential size. Interestingly, it is possible to decide in polynomial time if the lcs exists.

Pearl and Dechter (1996) claimed that the d-separation criterion for conditional independence in acyclic causal networks also applies to networks of discrete variables that have feedback cycles, provided that the variables of the system are uniquely determined by the random disturbances. I show by example that this is not true in general. Some condition stronger than uniqueness is needed, such as the existence of a causal dynamics guaranteed to lead to the unique solution.

We investigate the space efficiency of a Propositional Knowledge Representation (PKR) formalism. Intuitively, the space efficiency of a formalism F in representing a certain piece of knowledge A, is the size of the shortest formula of F that represents A. In this paper we assume that knowledge is either a set of propositional interpretations (models) or a set of propositional formulae (theorems). We provide a formal way of talking about the relative ability of PKR formalisms to compactly represent a set of models or a set of theorems. We introduce two new compactness measures, the corresponding classes, and show that the relative space efficiency of a PKR formalism in representing models/theorems is directly related to such classes. In particular, we consider formalisms for nonmonotonic reasoning, such as circumscription and default logic, as well as belief revision operators and the stable model semantics for logic programs with negation. One interesting result is that formalisms with the same time complexity do not necessarily belong to the same space efficiency class.

Recently model checking representation and search techniques were shown to be efficiently applicable to planning, in particular to non-deterministic planning. Such planning approaches use Ordered Binary Decision Diagrams (OBDDs) to encode a planning domain as a non-deterministic finite automaton and then apply fast algorithms from model checking to search for a solution. OBDDs can effectively scale and can provide universal plans for complex planning domains. We are particularly interested in addressing the complexities arising in non-deterministic, multi-agent domains. In this article, we present UMOP, a new universal OBDD-based planning framework for non-deterministic, multi-agent domains. We introduce a new planning domain description language, NADL, to specify non-deterministic, multi-agent domains. The language contributes the explicit definition of controllable agents and uncontrollable environment agents. We describe the syntax and semantics of NADL and show how to build an efficient OBDD-based representation of an NADL description. The UMOP planning system uses NADL and different OBDD-based universal planning algorithms. It includes the previously developed strong and strong cyclic planning algorithms. In addition, we introduce our new optimistic planning algorithm that relaxes optimality guarantees and generates plausible universal plans in some domains where no strong nor strong cyclic solution exists. We present empirical results applying UMOP to domains ranging from deterministic and single-agent with no environment actions to non-deterministic and multi-agent with complex environment actions. UMOP is shown to be a rich and efficient planning system.

We show how to find a minimum weight loop cutset in a Bayesian network with high probability. Finding such a loop cutset is the first step in the method of conditioning for inference. Our randomized algorithm for finding a loop cutset outputs a minimum loop cutset after O(c 6^k kn) steps with probability at least 1 - (1 - 1/(6^k))^c6^k, where c > 1 is a constant specified by the user, k is the minimal size of a minimum weight loop cutset, and n is the number of vertices. We also show empirically that a variant of this algorithm often finds a loop cutset that is closer to the minimum weight loop cutset than the ones found by the best deterministic algorithms known.

We investigate the problem of reasoning in the propositional fragment of MBNF, the logic of minimal belief and negation as failure introduced by Lifschitz, which can be considered as a unifying framework for several nonmonotonic formalisms, including default logic, autoepistemic logic, circumscription, epistemic queries, and logic programming. We characterize the complexity and provide algorithms for reasoning in propositional MBNF. In particular, we show that entailment in propositional MBNF lies at the third level of the polynomial hierarchy, hence it is harder than reasoning in all the above mentioned propositional formalisms for nonmonotonic reasoning. We also prove the exact correspondence between negation as failure in MBNF and negative introspection in Moore's autoepistemic logic.

Multi-Agent Systems (MAS) promise to offer solutions to problems where established, older paradigms fall short. In order to validate such claims that are repeatedly made in software agent publications, empirical in-depth studies of advantages and weaknesses of multi-agent solutions versus conventional ones in practical applications are needed. Climate control in large buildings is one application area where multi-agent systems, and market-oriented programming in particular, have been reported to be very successful, although central control solutions are still the standard practice. We have therefore constructed and implemented a variety of market designs for this problem, as well as different standard control engineering solutions. This article gives a detailed analysis and comparison, so as to learn about differences between standard versus agent approaches, and yielding new insights about benefits and limitations of computational markets. An important outcome is that "local information plus market communication produces global control".

There are two distinct approaches to solving reinforcement learning problems, namely, searching in value function space and searching in policy space. Temporal difference methods and evolutionary algorithms are well-known examples of these approaches. Kaelbling, Littman and Moore recently provided an informative survey of temporal difference methods. This article focuses on the application of evolutionary algorithms to the reinforcement learning problem, emphasizing alternative policy representations, credit assignment methods, and problem-specific genetic operators. Strengths and weaknesses of the evolutionary approach to reinforcement learning are presented, along with a survey of representative applications.

In many real-world learning tasks, it is expensive to acquire a sufficient number of labeled examples for training. This paper investigates methods for reducing annotation cost by `sample selection'. In this approach, during training the learning program examines many unlabeled examples and selects for labeling only those that are most informative at each stage. This avoids redundantly labeling examples that contribute little new information. Our work follows on previous research on Query By Committee, extending the committee-based paradigm to the context of probabilistic classification. We describe a family of empirical methods for committee-based sample selection in probabilistic classification models, which evaluate the informativeness of an example by measuring the degree of disagreement between several model variants. These variants (the committee) are drawn randomly from a probability distribution conditioned by the training set labeled so far. The method was applied to the real-world natural language processing task of stochastic part-of-speech tagging. We find that all variants of the method achieve a significant reduction in annotation cost, although their computational efficiency differs. In particular, the simplest variant, a two member committee with no parameters to tune, gives excellent results. We also show that sample selection yields a significant reduction in the size of the model used by the tagger.