Many AI tasks, such as product configuration, decision support, and the construction of autonomous agents, involve a process of constrained optimization, that is, optimization of behavior or choices subject to given constraints. In this paper we present an approach for constrained optimization based on a set of hard constraints and a preference ordering represented using a CP-network - a graphical model for representing qualitative preference information. This approach offers both pragmatic and computational advantages. First, it provides a convenient and intuitive tool for specifying the problem, and in particular, the decision maker's preferences. Second, it provides an algorithm for finding the most preferred feasible outcomes that has the following anytime property: the set of preferred feasible outcomes are enumerated without backtracking. In particular, the first feasible solution generated by this algorithm is optimal.

This paper studies a variant of axioms originally developed by Shafer and Shenoy (1988). It is investigated which extra assumptions are needed to perform the local computations in a HUGIN-like architecture (Jensen et al. 1990) or in the architecture of Lauritzen and Spiegelhalter (1988). In particular it is shown that propagation of belief functions can be performed in these architectures. Keywords: articial intelligence, belief function, constraint propagation, expert system, probability propagation, valuation-based system. 1 Introduction An important development in articial intelligence is associated with an abstract theory of local computation known as the Shafer{Shenoy axioms (Shafer and Shenoy 1988; Shenoy and Shafer 1990). These describe in a very general setting how computations can be performed eciently and locally in a variety of problems, just if a few simple conditions are satised. Even though the axioms were developed to formalize computation with belief functions (Shaf...

We survey the literature on methods for inference and learning in Bayesian Networks composed of discrete and continuous nodes, in which the continuous nodes have a multivariate Gaussian distribution, whose mean and variance depends on the values of the discrete nodes. We also briefly consider hybrid Dynamic Bayesian Networks, an extension of switching Kalman filters. This report is meant to summarize what is known at a sufficient level of detail to enable someone to implement the algorithms, but without dwelling on formalities.

We present a new approach to the solution of decision problems formulated as in- uence diagrams. The approach converts the inuence diagram into a simpler structure, the LImited Memory Inuence Diagram (LIMID), where only the requisite information for the computation of optimal policies is depicted. Because the requisite information is explicitly represented in the diagram, the evaluation procedure can take advantage of it. In this paper we show how to convert an inuence diagram to a LIMID and describe the procedure for nding an optimal strategy. Our approach can yield signicant savings of memory and computational time when compared to traditional methods. 1 INTRODUCTION Inuence Diagrams (IDs) were introduced by Howard and Matheson (1981) as a compact representation of decision problems. Since then, various authors have attempted to formalize their approach and develop algorithms for evaluating IDs. Olmsted (1983) and Shachter (1986) initiated research in this di...

We introduce the notion of LImited Memory Influence Diagram (LIMID) to describe multi-stage decision problems where the traditional assumption of no forgetting is relaxed. This can be relevant in situations with multiple decision makers or when decisions must be prescribed under memory constraints, such as e.g. in partially observed Markov decision processes (POMDPs). We give an algorithm for improving any given strategy by local computation of single policy updates. We investigate conditions for the resulting strategy to be optimal. As a consequence we also obtain an efficient algorithm for solving traditional influence diagrams. Key words: Influence diagram; junction tree; local computation; message passing; optimal strategies; partially observed Markov decision process, POMDP, single policy updating. 1 Introduction This article is concerned with finding optimal strategies in multi-stage decision problems involving uncertainty. In accordance with classical decision theo...

Introduction In recent years there are a number of areas where graphical models have served successfully in the process of understanding, formulating, and solving problems. Although the early papers on graphical models were dealing with undirected graphs (Darroch, Lauritzen, and Speed 1980), recent applications of graphical models have predominantly been based on directed graphical models, also known as recursive models (Wermuth and Lauritzen 1983) or Bayesian networks, a term coined by Pearl (1986). This will also be reected in the emphasis of the present chapter which will describe new areas of application and methodology for Bayesian networks, not otherwise well represented in this volume. This means in particular that we will not discuss the application of Bayesian networks to problems of genetic computation and problems of causal reasoning and discovery. The versatility of Bayesian network methodology has in particular been demonstrated in connection with

Bayesian networks (BNs) are a compact representation of a joint probability distribution. In this paper we show how they can be used for modeling other agents in the environment. More precisely we will have special attention to the problem of large state spaces and incomplete information. For our experiments we will consider the robotic soccer simulation for several reasons explained. Robotic soccer clients will learn through Q-learning, a form of reinforcement learning. The long-term goal of this research is to dene generic techniques that allow agents to learn in large-scaled multi-agent systems.

this paper we look at graphical models from this point of view. We introduce various kinds of graphical models, and the comprehensibility of their syntax and semantics is in focus

In descriptive decision and game theory, one speci es a model of a situation faced by agents and uses the model to predict or explain their behavior. We present Inuence Diagram Networks, a language for descriptive decision and game theory that is based on graphical models. Our language relaxes the assumption traditionally used in economics that beliefs of agents are consistent, i.e. conditioned on a common prior distribution. In the single-agent case one can model situations in which the agent has an incorrect model of the way the world works, or in which a modeler has uncertainty about the agent's model. In the multi-agent case, one can model agents' uncertain beliefs about other agents' decision-making models. We present an algorithm that computes the actions of agents under the assumption that they are rational with respect to their own model, but not necessarily with respect to the real world.