Decision Theory Meets Linear Optimization Beyond Computation

Jansen, Christoph and Schollmeyer, Georg and Augustin, Thomas (2017) Decision Theory Meets Linear Optimization Beyond Computation. In: Symbolic and Quantitative Approaches to Reasoning with Uncertainty : 14th European Conference, ECSQARU 2017, Lugano, Switzerland, July 10–14, 2017, Proceedings. Lecture Notes in Computer Science . Springer, Cham, pp. 329-339. ISBN 9783319615806

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The paper is concerned with decision making under complex uncertainty. We consider the Hodges and Lehmann-criterion relying on uncertain classical probabilities and Walley’s maximality relying on imprecise probabilities. We present linear programming based approaches for computing optimal acts as well as for determining least favorable prior distributions in finite decision settings. Further, we apply results from duality theory of linear programming in order to provide theoretical insights into certain characteristics of these optimal solutions. Particularly, we characterize conditions under which randomization pays out when defining optimality in terms of the Gamma-Maximin criterion and investigate how these conditions relate to least favorable priors.

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06 Jun 2024 14:45
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07 Jun 2024 00:17