This book provides different mathematical frameworks for addressing supervised learning. It is based on a workshop held under the auspices of the Center for Nonlinear Studies at Los Alamos and the Santa Fe Institute in the summer of 1992.

This volume grew out of a workshop designed to bring together researchers from different fields and includes contributions from workers in Bayesian analysis, machine learning, neural nets, PAC and VC theory, classical sampling theory statistics and the statistical physics of learning. The contributions present a bird's-eye view of the subject.

Prescriptive Bayesian decision making has reached a high level of maturity and is well-supported algorithmically. However, experimental data shows that real decision makers choose such Bayes-optimal decisions surprisingly infrequently, often making decisions that are badly sub-optimal. So prevalent is such imperfect decision-making that it should be accepted as an inherent feature of real decision makers living within interacting societies. To date such societies have been investigated from an economic and gametheoretic perspective, and even to a degree from a physics perspective. However, little research has been done from the perspective of computer science and associated disciplines like machine learning, information theory and neuroscience. This book is a major contribution to such research. Some of the particular topics addressed include: How should we formalise rational decision making of a single imperfect decision maker? Does the answer change for a system of imperfect decision makers? Can we extend existing prescriptive theories for perfect decision makers to make them useful for imperfect ones? How can we exploit the relation of these problems to the control under varying and uncertain resources constraints as well as to the problem of the computational decision making? What can we learn from natural, engineered, and social systems to help us address these issues?

This volume focuses on uncovering the fundamental forces underlying dynamic decision making among multiple interacting, imperfect and selfish decision makers. The chapters are written by leading experts from different disciplines, all considering the many sources of imperfection in decision making, and always with an eye to decreasing the myriad discrepancies between theory and real world human decision making. Topics addressed include uncertainty, deliberation cost and the complexity arising from the inherent large computational scale of decision making in these systems. In particular, analyses and experiments are presented which concern: • task allocation to maximize “the wisdom of the crowd”; • design of a society of “edutainment” robots who account for one anothers’ emotional states; • recognizing and counteracting seemingly non-rational human decision making; • coping with extreme scale when learning causality in networks; • efficiently incorporating expert knowledge in personalized medicine; • the effects of personality on risky decision making. The volume is a valuable source for researchers, graduate students and practitioners in machine learning, stochastic control, robotics, and economics, among other fields.

In this chapter an analysis of the behavior of an arbitrary (perhaps massive) collective of computational processes in terms of an associated "world" utility function is presented We concentrate on the situation where each process in the collective can be viewed as though it were striving to maximize its own private utility function. For such situations the central design issue is how to initialize/update the collective's structure, and in particular the private utility functions, so as to induce the overall collective to behave in a way that has large values of the world utility. Traditional "team game" approaches to this problem simply set each private utility function equal to the world utility function. The "Collective Intelligence" (COIN) framework is a semi-formal set of heuristics that recently have been used to construct private utility. functions that in many experiments have resulted in world utility values up to orders of magnitude superior to that ensuing from use of the team game utility. In this paper we introduce a formal mathematics for analyzing and designing collectives. We also use this mathematics to suggest new private utilities that should outperform the COIN heuristics in certain kinds of domains. In accompanying work we use that mathematics to explain previous experimental results concerning the superiority of COIN heuristics. In that accompanying work we also use the mathematics to make numerical predictions, some of which we then test. In this way these two papers establish the study of collectives as a proper science, involving theory, explanation of old experiments, prediction concerning new experiments, and engineering insights.

Prescriptive Bayesian decision making has reached a high level of maturity and is well-supported algorithmically. However, experimental data shows that real decision makers choose such Bayes-optimal decisions surprisingly infrequently, often making decisions that are badly sub-optimal. So prevalent is such imperfect decision-making that it should be accepted as an inherent feature of real decision makers living within interacting societies.

To date such societies have been investigated from an economic and gametheoretic perspective, and even to a degree from a physics perspective. However, little research has been done from the perspective of computer science and associated disciplines like machine learning, information theory and neuroscience. This book is a major contribution to such research.

Some of the particular topics addressed include: How should we formalise rational decision making of a single imperfect decision maker? Does the answer change for a system of imperfect decision makers? Can we extend existing prescriptive theories for perfect decision makers to make them useful for imperfect ones? How can we exploit the relation of these problems to the control under varying and uncertain resources constraints as well as to the problem of the computational decision making? What can we learn from natural, engineered, and social systems to help us address these issues?"

This volume focuses on uncovering the fundamental forces underlying dynamic decision making among multiple interacting, imperfect and selfish decision makers. The chapters are written by leading experts from different disciplines, all considering the many sources of imperfection in decision making, and always with an eye to decreasing the myriad discrepancies between theory and real world human decision making. Topics addressed include uncertainty, deliberation cost and the complexity arising from the inherent large computational scale of decision making in these systems. In particular, analyses and experiments are presented which concern: * task allocation to maximize "the wisdom of the crowd"; * design of a society of "edutainment" robots who account for one anothers' emotional states; * recognizing and counteracting seemingly non-rational human decision making; * coping with extreme scale when learning causality in networks; * efficiently incorporating expert knowledge in personalized medicine; * the effects of personality on risky decision making. The volume is a valuable source for researchers, graduate students and practitioners in machine learning, stochastic control, robotics, and economics, among other fields.