Inverse Parametric Optimization For Learning Utility Functions From Optimal And Satisficing Decisions

Inverse optimization is a method to determine optimization model parameters from observed decisions. Despite being a learning method, inverse optimization is not part of a data scientist's toolkit in practice, especially as many general-purpose machine learning packages are widely available as an alternative. In this dissertation, we examine and remedy two aspects of inverse optimization that prevent it from becoming more used by practitioners. These aspects include the alternative-based approach in inverse optimization modeling and the assumption that observations should be optimal. In the first part of the dissertation, we position inverse optimization as a learning method in analogy to supervised machine learning. The first part of this dissertation provides a starting point toward identifying the characteristics that make inverse optimization more efficient compared to general out-of-the-box supervised machine learning approaches, focusing on the problem of imputing the objective function of a parametric convex optimization problem. The second part of this dissertation provides an attribute-based perspective to inverse optimization modeling. Inverse attribute-based optimization imputes the importance of the decision attributes that result in minimally suboptimal decisions instead of imputing the importance of decisions. This perspective expands the range of inverse optimization applicability. We demonstrate that it facilitates the application of inverse optimization in assortment optimization, where changing product selections is a defining feature and accurate predictions of demand are essential. Finally, in the third part of the dissertation, we expand inverse parametric optimization to a more general setting where the assumption that the observations are optimal is relaxed to requiring only feasibility. The proposed inverse satisfaction method can deal with both feasible and minimally suboptimal solutions. We mathematically prove that the inverse satisfaction method provides statistically consistent estimates of the unknown parameters and can learn from both optimal and feasible decisions.

An introduction to decision making under uncertainty from a computational perspective, covering both theory and applications ranging from speech recognition to airborne collision avoidance. Many important problems involve decision making under uncertainty—that is, choosing actions based on often imperfect observations, with unknown outcomes. Designers of automated decision support systems must take into account the various sources of uncertainty while balancing the multiple objectives of the system. This book provides an introduction to the challenges of decision making under uncertainty from a computational perspective. It presents both the theory behind decision making models and algorithms and a collection of example applications that range from speech recognition to aircraft collision avoidance. Focusing on two methods for designing decision agents, planning and reinforcement learning, the book covers probabilistic models, introducing Bayesian networks as a graphical model that captures probabilistic relationships between variables; utility theory as a framework for understanding optimal decision making under uncertainty; Markov decision processes as a method for modeling sequential problems; model uncertainty; state uncertainty; and cooperative decision making involving multiple interacting agents. A series of applications shows how the theoretical concepts can be applied to systems for attribute-based person search, speech applications, collision avoidance, and unmanned aircraft persistent surveillance. Decision Making Under Uncertainty unifies research from different communities using consistent notation, and is accessible to students and researchers across engineering disciplines who have some prior exposure to probability theory and calculus. It can be used as a text for advanced undergraduate and graduate students in fields including computer science, aerospace and electrical engineering, and management science. It will also be a valuable professional reference for researchers in a variety of disciplines.

In a complex and uncertain world, humans and animals make decisions under the constraints of limited knowledge, resources, and time. Yet models of rational decision making in economics, cognitive science, biology, and other fields largely ignore these real constraints and instead assume agents with perfect information and unlimited time. About forty years ago, Herbert Simon challenged this view with his notion of "bounded rationality." Today, bounded rationality has become a fashionable term used for disparate views of reasoning. This book promotes bounded rationality as the key to understanding how real people make decisions. Using the concept of an "adaptive toolbox," a repertoire of fast and frugal rules for decision making under uncertainty, it attempts to impose more order and coherence on the idea of bounded rationality. The contributors view bounded rationality neither as optimization under constraints nor as the study of people's reasoning fallacies. The strategies in the adaptive toolbox dispense with optimization and, for the most part, with calculations of probabilities and utilities. The book extends the concept of bounded rationality from cognitive tools to emotions; it analyzes social norms, imitation, and other cultural tools as rational strategies; and it shows how smart heuristics can exploit the structure of environments.

Researchers working with nonlinear programming often claim "the word is non linear" indicating that real applications require nonlinear modeling. The same is true for other areas such as multi-objective programming (there are always several goals in a real application), stochastic programming (all data is uncer tain and therefore stochastic models should be used), and so forth. In this spirit we claim: The word is multilevel. In many decision processes there is a hierarchy of decision makers, and decisions are made at different levels in this hierarchy. One way to handle such hierar chies is to focus on one level and include other levels' behaviors as assumptions. Multilevel programming is the research area that focuses on the whole hierar chy structure. In terms of modeling, the constraint domain associated with a multilevel programming problem is implicitly determined by a series of opti mization problems which must be solved in a predetermined sequence. If only two levels are considered, we have one leader (associated with the upper level) and one follower (associated with the lower level).

Herbert Simon's classic work on artificial intelligence in the expanded and updated third edition from 1996, with a new introduction by John E. Laird. Herbert Simon's classic and influential The Sciences of the Artificial declares definitively that there can be a science not only of natural phenomena but also of what is artificial. Exploring the commonalities of artificial systems, including economic systems, the business firm, artificial intelligence, complex engineering projects, and social plans, Simon argues that designed systems are a valid field of study, and he proposes a science of design. For this third edition, originally published in 1996, Simon added new material that takes into account advances in cognitive psychology and the science of design while confirming and extending the book's basic thesis: that a physical symbol system has the necessary and sufficient means for intelligent action. Simon won the Nobel Prize for Economics in 1978 for his research into the decision-making process within economic organizations and the Turing Award (considered by some the computer science equivalent to the Nobel) with Allen Newell in 1975 for contributions to artificial intelligence, the psychology of human cognition, and list processing. The Sciences of the Artificial distills the essence of Simon's thought accessibly and coherently. This reissue of the third edition makes a pioneering work available to a new audience.

This handbook in two parts covers key topics of the theory of financial decision making. Some of the papers discuss real applications or case studies as well. There are a number of new papers that have never been published before especially in Part II.Part I is concerned with Decision Making Under Uncertainty. This includes subsections on Arbitrage, Utility Theory, Risk Aversion and Static Portfolio Theory, and Stochastic Dominance. Part II is concerned with Dynamic Modeling that is the transition for static decision making to multiperiod decision making. The analysis starts with Risk Measures and then discusses Dynamic Portfolio Theory, Tactical Asset Allocation and Asset-Liability Management Using Utility and Goal Based Consumption-Investment Decision Models.A comprehensive set of problems both computational and review and mind expanding with many unsolved problems are in an accompanying problems book. The handbook plus the book of problems form a very strong set of materials for PhD and Masters courses both as the main or as supplementary text in finance theory, financial decision making and portfolio theory. For researchers, it is a valuable resource being an up to date treatment of topics in the classic books on these topics by Johnathan Ingersoll in 1988, and William Ziemba and Raymond Vickson in 1975 (updated 2 nd edition published in 2006).

This work, a paradigm for modelling decision-making under uncertainty, describes the general theory and its relationship to planning, repeated choice problems, inductive inference, and learning; and highlights its mathematical and philosophical foundations.

Multiobjective optimization deals with solving problems having not only one, but multiple, often conflicting, criteria. Such problems can arise in practically every field of science, engineering and business, and the need for efficient and reliable solution methods is increasing. The task is challenging due to the fact that, instead of a single optimal solution, multiobjective optimization results in a number of solutions with different trade-offs among criteria, also known as Pareto optimal or efficient solutions. Hence, a decision maker is needed to provide additional preference information and to identify the most satisfactory solution. Depending on the paradigm used, such information may be introduced before, during, or after the optimization process. Clearly, research and application in multiobjective optimization involve expertise in optimization as well as in decision support. This state-of-the-art survey originates from the International Seminar on Practical Approaches to Multiobjective Optimization, held in Dagstuhl Castle, Germany, in December 2006, which brought together leading experts from various contemporary multiobjective optimization fields, including evolutionary multiobjective optimization (EMO), multiple criteria decision making (MCDM) and multiple criteria decision aiding (MCDA). This book gives a unique and detailed account of the current status of research and applications in the field of multiobjective optimization. It contains 16 chapters grouped in the following 5 thematic sections: Basics on Multiobjective Optimization; Recent Interactive and Preference-Based Approaches; Visualization of Solutions; Modelling, Implementation and Applications; and Quality Assessment, Learning, and Future Challenges.