Artificial Intelligence
A primal-dual interior point algorithm for linear programming
Progress in Mathematical Programming Interior-point and related methods
2U: an exact interval propagation algorithm for polytrees with binary variables
Artificial Intelligence
Bounded-parameter Markov decision process
Artificial Intelligence
Dynamic Programming and Optimal Control
Dynamic Programming and Optimal Control
A new polynomial-time algorithm for linear programming
STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
Dynamic Programming
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
Algebraic Markov decision processes
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
Graphical models for imprecise probabilities
International Journal of Approximate Reasoning
Probabilistic reasoning about actions in nonmonotonic causal theories
UAI'03 Proceedings of the Nineteenth conference on Uncertainty in Artificial Intelligence
Unifying nondeterministic and probabilistic planning through imprecise markov decision processes
IBERAMIA-SBIA'06 Proceedings of the 2nd international joint conference, and Proceedings of the 10th Ibero-American Conference on AI 18th Brazilian conference on Advances in Artificial Intelligence
Markov decision processes from colored Petri nets
SBIA'10 Proceedings of the 20th Brazilian conference on Advances in artificial intelligence
Sequential decision making with partially ordered preferences
Artificial Intelligence
Efficient solutions to factored MDPs with imprecise transition probabilities
Artificial Intelligence
International Journal of Approximate Reasoning
Evidential Markov decision processes
ECSQARU'11 Proceedings of the 11th European conference on Symbolic and quantitative approaches to reasoning with uncertainty
Shortest stochastic path with risk sensitive evaluation
MICAI'12 Proceedings of the 11th Mexican international conference on Advances in Artificial Intelligence - Volume Part I
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Two noteworthy models of planning in AI are probabilistic planning (based on MDPs and its generalizations) and nondeterministic planning (mainly based on model checking). In this paper we: (1) show that probabilistic and nondeterministic planning are extremes of a rich continuum of problems that deal simultaneously with risk and (Knightian) uncertainty; (2) obtain a unifying model for these problems using imprecise MDPs; (3) derive a simplified Bellman's principle of optimality for our model; and (4) show how to adapt and analyze state-of-art algorithms such as (L)RTDP and LDFS in this unifying setup. We discuss examples and connections to various proposals for planning under (general) uncertainty.