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Free Energy and the Generalized Optimality Equations for Sequential Decision Making

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http://pubman.mpdl.mpg.de/cone/persons/resource/persons84121

Ortega,  PA
Research Group Sensorimotor Learning and Decision-Making, Max Planck Institute for Biological Cybernetics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons83827

Braun,  DA
Research Group Sensorimotor Learning and Decision-Making, Max Planck Institute for Biological Cybernetics, Max Planck Society;

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Citation

Ortega, P., & Braun, D. (2012). Free Energy and the Generalized Optimality Equations for Sequential Decision Making. In 10th European Workshop on Reinforcement Learning (EWRL 2012) (pp. 1-10).


Cite as: http://hdl.handle.net/11858/00-001M-0000-0013-B6C2-2
Abstract
The free energy functional has recently been proposed as a variational principle for bounded rational decision-making, since it instantiates a natural trade-off between utility gains and information processing costs that can be axiomatically derived. Here we apply the free energy principle to general decision trees that include both adversarial and stochastic environments. We derive generalized sequential optimality equations that not only include the Bellman optimality equations as a limit case, but also lead to well-known decision-rules such as Expectimax, Minimax and Expectiminimax. We show how these decision-rules can be derived from a single free energy principle that assigns a resource parameter to each node in the decision tree. These resource parameters express a concrete computational cost that can be measured as the amount of samples that are needed from the distribution that belongs to each node. The free energy principle therefore provides the normative basis for generalized optimality equations that account for both adversarial and stochastic environments.