Decision Making under Uncertainty through Extending Influence Diagrams with Interval-valued Parameters

Influence Diagrams (IDs) are one of the most commonly used graphical and mathematical decision models for reasoning under uncertainty. In conventional IDs, both probabilities representing beliefs and utilities representing preferences of decision makers are precise point-valued parameters. However, it is usually difficult or even impossible to directly provide such parameters. In this paper, we extend conventional IDs to allow IDs with interval-valued parameters (IIDs), and develop a counterpart method of Copper’s evaluation method to evaluate IIDs. IIDs avoid the difficulties attached to the specification of precise parameters and provide the capability to model decision making processes in a situation that the precise parameters cannot be specified. The counterpart method to Copper’s evaluation method reduces the evaluation of IIDs into inference problems of IBNs. An algorithm based on the approximate inference of IBNs is proposed, extensive experiments are conducted. The experimental results indicate that the proposed algorithm can find the optimal strategies effectively in IIDs, and the interval-valued expected utilities obtained by proposed algorithm are contained in those obtained by exact evaluating algorithms

Solving Limited Memory Influence Diagrams

We present a new algorithm for exactly solving decision making problems represented as influence diagrams. We do not require the usual assumptions of no forgetting and regularity; this allows us to solve problems with simultaneous decisions and limited information. The algorithm is empirically shown to outperform a state-of-the-art algorithm on randomly generated problems of up to 150 variables and $10^{64}$ solutions. We show that the problem is NP-hard even if the underlying graph structure of the problem has small treewidth and the variables take on a bounded number of states, but that a fully polynomial time approximation scheme exists for these cases. Moreover, we show that the bound on the number of states is a necessary condition for any efficient approximation scheme.Comment: 43 pages, 8 figure

Game Theory and Prescriptive Analytics for Naval Wargaming Battle Management Aids

NPS NRP Technical ReportThe Navy is taking advantage of advances in computational technologies and data analytic methods to automate and enhance tactical decisions and support warfighters in highly complex combat environments. Novel automated techniques offer opportunities to support the tactical warfighter through enhanced situational awareness, automated reasoning and problem-solving, and faster decision timelines. This study will investigate how game theory and prescriptive analytics methods can be used to develop real-time wargaming capabilities to support warfighters in their ability to explore and evaluate the possible consequences of different tactical COAs to improve tactical missions. This study will develop a conceptual design of a real-time tactical wargaming capability. This study will explore data analytic methods including game theory, prescriptive analytics, and artificial intelligence (AI) to evaluate their potential to support real-time wargaming.N2/N6 - Information WarfareThis research is supported by funding from the Naval Postgraduate School, Naval Research Program (PE 0605853N/2098). https://nps.edu/nrpChief of Naval Operations (CNO)Approved for public release. Distribution is unlimited.