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Conference Paper

A Nonparametric Conjugate Prior Distribution for the Maximizing Argument of a Noisy Function

MPS-Authors
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/persons84522

Grau-Moya,  J
Research Group Sensorimotor Learning and Decision-Making, Max Planck Institute for Biological Cybernetics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons84447

Genewein,  T
Department Human Perception, Cognition and Action, Max Planck Institute for Biological Cybernetics, Max Planck Society;
Research Group Sensorimotor Learning and Decision-Making, Max Planck Institute for Biological Cybernetics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons83792

Balduzzi,  D
Department Empirical Inference, 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., Grau-Moya, J., Genewein, T., Balduzzi, D., & Braun, D. (2012). A Nonparametric Conjugate Prior Distribution for the Maximizing Argument of a Noisy Function. In Advances in Neural Information Processing Systems 25 (pp. 3014-3022).


Cite as: http://hdl.handle.net/11858/00-001M-0000-0013-B548-F
Abstract
We propose a novel Bayesian approach to solve stochastic optimization problems that involve finding extrema of noisy, nonlinear functions. Previous work has focused on representing possible functions explicitly, which leads to a two-step procedure of first, doing inference over the function space and second, finding the extrema of these functions. Here we skip the representation step and directly model the distribution over extrema. To this end, we devise a non-parametric conjugate prior where the natural parameter corresponds to a given kernel function and the sufficient statistic is composed of the observed function values. The resulting posterior distribution directly captures the uncertainty over the maximum of the unknown function.