Planning and acting in partially observable stochastic domains
Artificial Intelligence
Markov Decision Processes: Discrete Stochastic Dynamic Programming
Markov Decision Processes: Discrete Stochastic Dynamic Programming
A Comparison of Axiomatic Approaches to Qualitative Decision Making Using Possibility Theory
UAI '01 Proceedings of the 17th Conference in Uncertainty in Artificial Intelligence
Preference-based search and multi-criteria optimization
Eighteenth national conference on Artificial intelligence
Constraint solving over semirings
IJCAI'95 Proceedings of the 14th international joint conference on Artificial intelligence - Volume 1
Great expectations: part I: on the customizability of generalized expected utility
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
Great expectations: part II: generalized expected utility as a universal decision rule
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
Possibility theory as a basis for qualitative decision theory
IJCAI'95 Proceedings of the 14th international joint conference on Artificial intelligence - Volume 2
UAI'99 Proceedings of the Fifteenth conference on Uncertainty in artificial intelligence
Qualitative MDPs and POMDPs: an order-of-magnitude approximation
UAI'02 Proceedings of the Eighteenth conference on Uncertainty in artificial intelligence
Plausibility measures: a user's guide
UAI'95 Proceedings of the Eleventh conference on Uncertainty in artificial intelligence
An order of magnitude calculus
UAI'95 Proceedings of the Eleventh conference on Uncertainty in artificial intelligence
Dioïds and semirings: Links to fuzzy sets and other applications
Fuzzy Sets and Systems
Towards a formal framework for multi-objective multiagent planning
Proceedings of the 6th international joint conference on Autonomous agents and multiagent systems
Decision with uncertainties, feasibilities, and utilities: towards a unified algebraic framework
Proceedings of the 2006 conference on ECAI 2006: 17th European Conference on Artificial Intelligence August 29 -- September 1, 2006, Riva del Garda, Italy
An Axiomatic Approach to Qualitative Decision Theory with Binary Possibilistic Utility
Proceedings of the 2006 conference on ECAI 2006: 17th European Conference on Artificial Intelligence August 29 -- September 1, 2006, Riva del Garda, Italy
An algebraic graphical model for decision with uncertainties, feasibilities, and utilities
Journal of Artificial Intelligence Research
Planning under risk and Knightian uncertainty
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
Evidential Markov decision processes
ECSQARU'11 Proceedings of the 11th European conference on Symbolic and quantitative approaches to reasoning with uncertainty
Dominance rules for the choquet integral in multiobjective dynamic programming
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
Vector-Value Markov Decision Process for multi-objective stochastic path planning
International Journal of Hybrid Intelligent Systems
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In this paper, we provide an algebraic approach to Markov Decision Processes (MDPs), which allows a unified treatment of MDPs and includes many existing models (quantitative or qualitative) as particular cases. In algebraic MDPs, rewards are expressed in a semiring structure, uncertainty is represented by a decomposable plausibility measure valued on a second semiring structure, and preferences over policies are represented by Generalized Expected Utility. We recast the problem of finding an optimal policy at a finite horizon as an algebraic path problem in a decision rule graph where arcs are valued by functions, which justifies the use of the Jacobi algorithm to solve algebraic Bellman equations. In order to show the potential of this general approach, we exhibit new variations of MDPs, admitting complete or partial preference structures, as well as probabilistic or possibilistic representation of uncertainty.