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A Nonparametric Conjugate Prior Distribution for the Maximizing Argument of a Noisy Function
Pedro Ortega · Tim Genewein · Jordi Grau-Moya · David Balduzzi · Daniel A Braun

Mon Dec 03 07:00 PM -- 12:00 AM (PST) @ Harrah’s Special Events Center 2nd Floor

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.

Author Information

Pedro Ortega (DeepMind)
Tim Genewein (Max-Planck Institute)
Jordi Grau-Moya (Max Planck Institute)
David Balduzzi (Victoria University Wellington)
Daniel A Braun (University of Cambridge)

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