An axiomatic framework for influence diagram computation with partially ordered preferences

Abstract This paper presents an axiomatic framework for influence diagram computation, which allows reasoning with partially ordered values of utility. We show how an algorithm based on sequential variable elimination can be used to compute the set of maximal values of expected utility (up to an equivalence relation). Formalisms subsumed by the framework include decision making under uncertainty based on multi-objective utility, or on interval-valued utilities, as well as a more qualitative decision theory based on order of magnitude probabilities and utilities. Consequently, we also introduce the order of magnitude influence diagram to model and solve partially specified sequential decision problems when only qualitative (or imprecise) information is available.

[1]  Steffen L. Lauritzen,et al.  Representing and Solving Decision Problems with Limited Information , 2001, Manag. Sci..

[2]  Frank Jensen,et al.  From Influence Diagrams to junction Trees , 1994, UAI.

[3]  Patrice Perny,et al.  Algebraic Markov Decision Processes , 2005, IJCAI.

[4]  Rina Dechter,et al.  A New Perspective on Algorithms for Optimizing Policies under Uncertainty , 2000, AIPS.

[5]  Joseph Y. Halpern,et al.  Great expectations: part I: on the customizability of generalized expected utility , 2003, IJCAI 2003.

[6]  Prakash P. Shenoy,et al.  Valuation-Based Systems for Bayesian Decision Analysis , 1992, Oper. Res..

[7]  Blai Bonet,et al.  Qualitative MDPs and POMDPs: An Order-Of-Magnitude Approximation , 2002, UAI.

[8]  Fabio Gagliardi Cozman,et al.  Sequential decision making with partially ordered preferences , 2011, Artif. Intell..

[9]  Finn V. Jensen,et al.  Bayesian Networks and Decision Graphs , 2001, Statistics for Engineering and Information Science.

[10]  Rina Dechter,et al.  AND/OR Branch-and-Bound search for combinatorial optimization in graphical models , 2009, Artif. Intell..

[11]  Denis Deratani Mauá,et al.  Solving Limited Memory Influence Diagrams , 2011, J. Artif. Intell. Res..

[12]  Qiang Ji,et al.  Strategy Selection in Influence Diagrams using Imprecise Probabilities , 2008, UAI.

[13]  Prakash P. Shenoy,et al.  Valuation network representation and solution of asymmetric decision problems , 2000, Eur. J. Oper. Res..

[14]  Nic Wilson,et al.  Multi-Objective Constraint Optimization with Tradeoffs , 2013, CP.

[15]  Nic Wilson,et al.  Order-of-Magnitude Influence Diagrams , 2011, UAI.

[16]  Régis Sabbadin,et al.  Complexity results and algorithms for possibilistic influence diagrams , 2008, Artif. Intell..

[17]  Rafael Cabañas,et al.  Evaluating interval-valued influence diagrams , 2017, Int. J. Approx. Reason..

[18]  Nic Wilson,et al.  Multi-objective Influence Diagrams , 2012, UAI.

[19]  Judea Pearl,et al.  Qualitative Probabilities for Default Reasoning, Belief Revision, and Causal Modeling , 1996, Artif. Intell..

[20]  Thomas Schiex,et al.  Sequential Decision-Making Problems - Representation and Solution , 2009 .

[21]  Nic Wilson,et al.  An Axiomatic Framework for Influence Diagram Computation with Partially Ordered Utilities , 2012, KR.

[22]  Luis J. Rodríguez-Muñiz,et al.  Influence diagrams with super value nodes involving imprecise information , 2007, Eur. J. Oper. Res..

[23]  Rina Dechter,et al.  Memory intensive AND/OR search for combinatorial optimization in graphical models , 2009, Artif. Intell..

[24]  Wolfgang Spohn,et al.  Ordinal Conditional Functions: A Dynamic Theory of Epistemic States , 1988 .

[25]  Nic Wilson,et al.  Enabling local computation for partially ordered preferences , 2010, Constraints.

[26]  Moisés Goldszmidt,et al.  On the Relation between Kappa Calculus and Probabilistic Reasoning , 1994, UAI.

[27]  Jürg Kohlas.  Information algebras - generic structures for inference , 2003, Discrete mathematics and theoretical computer science.

[28]  Yacov Y. Haimes,et al.  Influence diagrams with multiple objectives and tradeoff analysis , 2004, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[29]  Enrico Fagiuoli,et al.  A note about redundancy in influence diagrams , 1998, Int. J. Approx. Reason..

[30]  Ronald A. Howard,et al.  Influence Diagrams , 2005, Decis. Anal..

[31]  Rina Dechter,et al.  Constraint Processing , 1995, Lecture Notes in Computer Science.

[32]  Ross D. Shachter,et al.  Fusion and Propagation with Multiple Observations in Belief Networks , 1991, Artif. Intell..

[33]  Denis Deratani Mauá,et al.  Updating credal networks is approximable in polynomial time , 2012, Int. J. Approx. Reason..

[34]  Gabriele Kern-Isberner.  A note on conditional logics and entropy , 1998, Int. J. Approx. Reason..

[35]  Nic Wilson,et al.  An Order of Magnitude Calculus , 1995, UAI.

[36]  Fabio Gagliardi Cozman,et al.  Credal networks , 2000, Artif. Intell..