2U: an exact interval propagation algorithm for polytrees with binary variables
Artificial Intelligence
Artificial Intelligence
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Representing and Solving Decision Problems with Limited Information
Management Science
Influence Diagrams for Team Decision Analysis
Decision Analysis
International Journal of Approximate Reasoning
Bayesian Networks and Decision Graphs
Bayesian Networks and Decision Graphs
Bounded policy iteration for decentralized POMDPs
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
The inferential complexity of Bayesian and credal networks
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
Generalized loopy 2U: A new algorithm for approximate inference in credal networks
International Journal of Approximate Reasoning
Optimizing fixed-size stochastic controllers for POMDPs and decentralized POMDPs
Autonomous Agents and Multi-Agent Systems
Influence diagrams with memory states: representation and algorithms
ADT'11 Proceedings of the Second international conference on Algorithmic decision theory
Welldefined decision scenarios
UAI'99 Proceedings of the Fifteenth conference on Uncertainty in artificial intelligence
Efficient value of information computation
UAI'99 Proceedings of the Fifteenth conference on Uncertainty in artificial intelligence
Solving POMDPs by searching in policy space
UAI'98 Proceedings of the Fourteenth conference on Uncertainty in artificial intelligence
UAI'98 Proceedings of the Fourteenth conference on Uncertainty in artificial intelligence
Solving limited memory influence diagrams
Journal of Artificial Intelligence Research
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Influence diagrams are intuitive and concise representations of structured decision problems. When the problem is non-Markovian, an optimal strategy can be exponentially large in the size of the diagram. We can avoid the inherent intractability by constraining the size of admissible strategies, giving rise to limited memory influence diagrams. A valuable question is then how small do strategies need to be to enable efficient optimal planning. Arguably, the smallest strategies one can conceive simply prescribe an action for each time step, without considering past decisions or observations. Previous work has shown that finding such optimal strategies even for polytree-shaped diagrams with ternary variables and a single value node is NP-hard, but the case of binary variables was left open. In this paper we address such a case, by first noting that optimal strategies can be obtained in polynomial time for polytree-shaped diagrams with binary variables and a single value node. We then show that the same problem is NP-hard if the diagram has multiple value nodes. These two results close the fixed-parameter complexity analysis of optimal strategy selection in influence diagrams parametrized by the shape of the diagram, the number of value nodes and the maximum variable cardinality.