Graphical representations for probabilistic relationships have recently received considerable attention in A1. Qualitative probabilistic networks abstract from the usual numeric representations by encoding only qualitative relationships, which are inequality constraints on the joint probability distribution over the variables. Although these constraints are insufficient to determine probabilities uniquely, they are designed to justify the deduction of a class of relative likelihood conclusions that imply useful decision-making properties. Two types of qualitative relationship are defined, each a probabilistic form of monotonicity constraint over a group of variables. Qualitative influences describe the direction of the relationship between two variables. Qualitative synergies describe interactions among influences. The probabilistic definitions chosen justify sound and efficient inference procedures based on graphical manipulations of the network. These procedures answer queries about qualitative relationships among variables separated in the network and determine structural properties of optimal assignments to decision variables.

This paper discusses techniques for performing efficient decision-theoretic planning. We give an overview of the drips decisiontheoretic refinement planning system, which uses abstraction to efficiently identify optimal plans. We present techniques for automatically generating search control information, which can significantly improve the planner's performance. We evaluate the efficiency of drips both with and without the search control rules on a complex medical planning problem and compare its performance to that of a branch-and-bound decision tree algorithm. 1 Introduction In the framework of decision-theoretic planning, uncertainty in the state of the world and in the effects of actions are represented with probabilities; and the planner 's goals, as well as tradeoffs among them, are represented with a utility function over outcomes. Given this representation, the objective is to find an optimal or near optimal plan. Finding the optimal plan requires comparing the expected utilit...

Standard algorithms for finding the shortest path in a graph require that the cost of a path be additive in edge costs, and typically assume that costs are deterministic. We consider the problem of uncertain edge costs, with potential probabilistic dependencies among the costs. Although these dependencies violate the standard dynamicprogramming decomposition, we identify a weaker stochastic consistency condition that justifies a generalized dynamic-programming approach based on stochastic dominance. We present a revised pathplanning algorithm and prove that it produces optimal paths under time-dependent uncertain costs. We illustrate the algorithm by applying it to a model of stochastic bus networks, and present sample performance results comparing it to some alternatives. For the case where all or some of the uncertainty is resolved during path traversal, we extend the algorithm to produce optimal policies. This report is based on a paper presented at the Eleventh Conference on Unc...

Most areas of engineering, science, and management use important tools based on probabilistic methods. The common thread of the entire spectrum of these tools is aiding in decision making under uncertainty: the choice of an interpretation of reality or the choice of a course of action. Although the importance of dealing with uncertainty in decision making is widely acknowledged, dissemination of probabilistic and decision-theoretic methods in Artificial Intelligence has been surprisingly slow. Opponents of probability theory have pointed out three major obstacles to applying it in computerized decision aids: (1) the counterintuitiveness of probabilistic inference, which makes it hard for system builders, experts, and users to translate knowledge into probabilistic form, create knowledge bases, and to interpret results; (2) the quantitative character of probability theory, which implies collection or assessment of vast quantities of numbers and, since these are not always readily available, raises questions about their quality; and (3) closely related to its quantitative character, the computational complexity of probabilistic inference. Its proponents, on the other hand, point

Meta-Level Control Agents plan in order to improve their performance, but planning takes time and other resources that can degrade performance. To plan effectively, an agent needs to be able to create high quality plans efficiently. Artificial intelligence planning techniques provide methods for generating plans, whereas decision theory offers expected utility as a measure for assessing plan quality, taking the value of each outcome and its likelihood into account. The benefits of combining artificial intelligence planning techniques and decision theory have long been recognized. However, these benefits will remain unrealized if the resulting decision-theoretic planners cannot generate plans with high expected utility in a timely fashion. In this dissertation, we address the meta-level control problem of allocating computation to make decision-theoretic planning efficient and effective. For efficiency, decision-theoretic planners iteratively approximate the complete solution to a decision problem: planners generate partially elaborated, abstract plans; only promising plans are further refined, and execution may begin before a plan with the highest expected

Abstract. We consider the problem of constructing a portfolio of finitely many assets whose returns are described by a discrete joint distribution. We propose mean–risk models which are solvable by linear programming and generate portfolios whose returns are nondominated in the sense of second-order stochastic dominance. Next, we develop a specialized parametric method for recovering the entire mean–risk efficient frontiers of these models and we illustrate its operation on a large data set involving thousands of assets and realizations. 1.

We consider stochastic networks' in which link travel times are dependent, discrete random variables. We present methods' for computing bounds' on path travel times using stochastic dominance relationships among link travel times, and discuss techniques for controlling tightness of the bounds'. We apply these methods' to shortest-path problems, show that the proposed algorithm can provide bounds' on the recommended path, and elaborate on extensions of the algorithm for demonstrating the anytime property.

Bounds of probability distributions are useful for many reasoning tasks, including resolving the qualitative ambiguities in qualitative probabilistic networks and searching the best path in stochastic transportation networks. This paper investigates a subclass of the state-space abstraction methods that are designed to approximately evaluate Bayesian networks. Taking advantage of particular stochastic-dominance relationships among random variables, these special methods aggregate states of random variables to obtain bounds of probability distributions at much reduced computational costs, thereby achieving high responsiveness of the overall system.

We study a very general setting, and propose a procedure for estimating the critical values of the extended Kolmogorov-Smirnov tests of First and Second Order Stochastic Dominance due to McFadden (1989) in the general k-prospect case. We allow for the observations to be generally serially dependent and, for the …rst time, we can accommodate general dependence amongst the prospects which are to be ranked. Also, the prospects may be the residuals from certain conditional models, opening the way for conditional ranking. We also propose a test of Prospect Stochastic Dominance. Our method is based on subsampling and we show that the resulting tests are consistent.

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