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A Minimum Relative Entropy Principle for Learning and Acting

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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. (2010). A Minimum Relative Entropy Principle for Learning and Acting. Journal of Artificial Intelligence Research, 38(1), 475-511. doi:10.1613/jair.3062.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0013-C00E-9
Abstract
This paper proposes a method to construct an adaptive agent that is universal with respect to a given class of experts, where each expert is designed specifically for a particular environment. This adaptive control problem is formalized as the problem of minimizing the relative entropy of the adaptive agent from the expert that is most suitable for the unknown environment. If the agent is a passive observer, then the optimal solution is the well-known Bayesian predictor. However, if the agent is active, then its past actions need to be treated as causal interventions on the I/O stream rather than normal probability conditions. Here it is shown that the solution to this new variational problem is given by a stochastic controller called the Bayesian control rule, which implements adaptive behavior as a mixture of experts. Furthermore, it is shown that under mild assumptions, the Bayesian control rule converges to the control law of the most suitable expert.