Sequential Decision-Making Problems

Numerous formalisms have been designed to model and solve decision-making problems. Some formalisms, such as constraint networks, can express "simple" decision problems, while others take into account uncertainties (probabilities, possibilities...), unfeasible decisions, and utilities (additive or not). In the first part of this book, we introduce a generic algebraic framework that encompasses and unifies a large number of such formalisms. This formalism, called the Plausibility–Feasibility–Utility (PFU) framework, is based on algebraic structures, graphical models, and sequences of quantifications. This work on knowledge representation is completed by a work on algorithms for answering queries formulated in the PFU framework. The algorithms defined are based on variable elimination or tree search, and work on a new generic architecture for local computations called multi-operator cluster DAGs.

Part I. Representing Decision-Making Problems in the Pfu Framework Chapter 1. Background Notation and Definitions Chapter 2. A Guided Tour of Frameworks for Decision-Making Chapter 3. A Generic Algebraic Structure for Sequential Decision-Making Chapter 4. Plausibility-Feasibility-Utility Networks Chapter 5. Queries on a PFU Network Part II. Generic Algorithms for Answering Pfu Queries Chapter 6. First Generic Algorithms Chapter 7. Structuring Multi-operator Queries Chapter 8. A Generic Structured Tree Search on the MCDAG Architecture Chapter 9. A Generic Solver for Answering PFU Queries Chapter 10. Conclusion Appendix A. Notation Appendix B. Proofs Appendix C. Concrete problem example: deployment and maintenance of a constellation of satellites Appendix D. DTD (Document Type Definition) of the XML format