It involves choosing optimally between different lines of action in various information contexts that range from perfectly knowing all aspects of the decision problem to having just partial knowledge about it. The physical context often includes other interacting autonomous systems, typically called agents. In this article, I focus on decision making in a multiagent context with partial information about the problem. Relevant research in this complex but realistic setting has converged around two complementary, general frameworks and also introduced myriad specializations on its way. I put the two frameworks, decentralized partially observable Markov decision process (Dec-POMDP) and the interactive partially observable Markov decision process (I-POMDP), in context and review the foundational algorithms for these frameworks, while briefly discussing the advances in their specializations.

Decision analysis and knowledge-based expert systems share some common goals. Both technologies are designed to improve human decision making; they attempt to do this by formalizing human expert knowledge so that it is amenable to mechanized reasoning. However, the technologies are based on rather different principles. Decision analysis is the application of the principles of decision theory supplemented with insights from the psychology of judgment. Expert systems, at least as we use this term here, involve the application of various logical and computational techniques of AI to the representation of human knowledge for automated inference.

Over the last few years, a method of reasoning using probabilities, variously called belief networks, Bayesian networks, knowledge maps, probabilistic causal networks, and so on, has become popular within the AI probability and uncertainty community. This method is best summarized in Judea Pearl's (1988) book, but the ideas are a product of many hands. I adopted Pearl's name, Bayesian networks, on the grounds that the name is completely neutral about the status of the networks (do they really represent beliefs, causality, or what?). I give an introduction to Bayesian networks for AI researchers with a limited grounding in probability theory. Over the last few years, this method of reasoning using probabilities has become popular within the AI probability and uncertainty community.

This article provides an overview of the field of qualitative decision theory: its motivating tasks and issues, its antecedents, and its prospects. Qualitative decision theory studies qualitative approaches to problems of decision making and their sound and effective reconciliation and integration with quantitative approaches. Although it inherits from a long tradition, the field offers a new focus on a number of important unanswered questions of common concern to AI, economics, law, psychology, and management. As developed by philosophers, economists, and mathematicians over some 300 years, these disciplines have developed many powerful ideas and techniques, which exert major influences over virtually all the biological, cognitive, and social sciences. Their uses range from providing mathematical foundations for microeconomics to daily application in a range of fields of practice, including finance, public policy, medicine, and now even automated device diagnosis.

Foremost Manufacturing Inc. (Union, NJ), a manufacturer of reflectors for lighting fixtures, has adopted a fuzzy logic-based application to produce quotations for customers in less time. The company is using a fuzzy system to produce bids in about 1.5 minutes, compared to an industry average of two weeks. Carnegie Group Inc. (Pittsburgh, PA) has developed a hybrid neural network/expert system for diagnostic situations where signal data and symbolic data must be combined to perform a definitive diagnosis and repair procedure. This technology was developed with funding from the National Science Foundation. Working with experts from Armco Steel (Middletown, OH), Carnegie Group developed a prototype system to diagnose chatter in a coldrolling mill.

The last few years have seen a surge in interest in the use of techniques from Bayesian decision theory to address problems in AI. Decision theory provides a normative framework for representing and reasoning about decision problems under uncertainty. Within the context of this framework, researchers in uncertainty in the AI community have been developing computational techniques for building rational agents and representations suited to engineering their knowledge bases. The articles cover the topics of inference in Bayesian networks, decision-theoretic planning, and qualitative decision theory. Here, I provide a brief introduction to Bayesian networks and then cover applications of Bayesian problem-solving techniques, knowledge-based model construction and structured representations, and the learning of graphic probability models.

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This article describes a theory of reasoning about uncertainty, baaed on a representation of states of certainty called endorsements The theory of endorsements is an alternative to numerical methods for reasoning about uncertainty, such as subjective Bayesian methods (Shortliffe and Buchanan, 1975; Duda, Hart, and Nilsson, 1976) and the Shafer-Dempster theory (Shafer, 1976). The fundamental concern with numerical representations of certainty is that they hide the reasoning that produces them and thus limit one's reasoning about uncertainty While numbers are easy to propagate over inferences, what the numbers mean is unclear The theory of endorsements provides a richer representation of the factors that affect certainty and supports multiple strategies for dealing with uncertainty. People's certainty of the past is limited by the fidelity of the devices that record it, their knowledge of the present is always incomplete, and their knowledge of the future is but speculation. Even though nothing is certain, people behave as if almost nothing is uncertain. They are adept at discounting uncertainty - making it go away.

The emergence of expert systems as one of the major areas of activity within AI has resulted in a rapid growth of interest within the AI community in issues relating to the management of uncertainty and evidential reasoning. During the past two years, in particular, the Dempster-Shafer theory of evidence has att,ract,ed considerable attention as a promising method of dealing with some of the basic problems arising in combination of evidence and data fusion. To develop an adequate understanding of this theory requires considerable effort and a good background in probability theory. There is, however, a simple way of approaching the Dempster-Shafer theory that only requires a minimal familiarity with relational models of data. For someone with a background in AI or database management, this approach has the advantage of relating in a natural way to the familiar framework of AI and databases.

The recent article by Roger C. Schank ("Where's the AI", AI Magazine, Winter, 1991) brought a broad nostalgic smile to my face. I believe that I am the unnamed Yale junior faculty member to whose work Prof. Schank alluded. Perhaps the intervening years have eradicated his memory of my name or, more likely, he wished to spare me the ignominy of serving as one of his principal strawmen. I, however, fully mindful of Oscar Wilde's observation that the only thing worse than being talked about is not being talked about, would not have been insulted by being identified. But, my purpose in writing is neither to defend my scientific integrity nor to dispel my anonymity.