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

Cédric Pralet, a graduate from a French engineering school with a PhD in Computer Sciences, is now working as a research engineer at ONERA (French Aerospace Lab).

Thomas Schiex is working at INRA (French Institute for Agronomical Research) on algorithms for constraint networks and graphical models, and their applications in computational biology.

Gérard Verfaillie's research activity at ONERA is related to models, methods, and tools for combinatorial optimization and constrained optimization, especially for planning and decision-making.