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Stochastic Control for Bayesian Neural Network Training

In this paper, we propose to leverage the Bayesian uncertainty information encoded in parameter distributions to inform the learning procedure for Bayesian models. We derive a first principle stochastic differential equation for the training dynamics of the mean and uncertainty parameter in the vari...

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Detalles Bibliográficos
Autores principales: Winkler, Ludwig, Ojeda, César, Opper, Manfred
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2022
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9407447/
https://www.ncbi.nlm.nih.gov/pubmed/36010761
http://dx.doi.org/10.3390/e24081097
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author Winkler, Ludwig
Ojeda, César
Opper, Manfred
author_facet Winkler, Ludwig
Ojeda, César
Opper, Manfred
author_sort Winkler, Ludwig
collection PubMed
description In this paper, we propose to leverage the Bayesian uncertainty information encoded in parameter distributions to inform the learning procedure for Bayesian models. We derive a first principle stochastic differential equation for the training dynamics of the mean and uncertainty parameter in the variational distributions. On the basis of the derived Bayesian stochastic differential equation, we apply the methodology of stochastic optimal control on the variational parameters to obtain individually controlled learning rates. We show that the resulting optimizer, StochControlSGD, is significantly more robust to large learning rates and can adaptively and individually control the learning rates of the variational parameters. The evolution of the control suggests separate and distinct dynamical behaviours in the training regimes for the mean and uncertainty parameters in Bayesian neural networks.
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spelling pubmed-94074472022-08-26 Stochastic Control for Bayesian Neural Network Training Winkler, Ludwig Ojeda, César Opper, Manfred Entropy (Basel) Article In this paper, we propose to leverage the Bayesian uncertainty information encoded in parameter distributions to inform the learning procedure for Bayesian models. We derive a first principle stochastic differential equation for the training dynamics of the mean and uncertainty parameter in the variational distributions. On the basis of the derived Bayesian stochastic differential equation, we apply the methodology of stochastic optimal control on the variational parameters to obtain individually controlled learning rates. We show that the resulting optimizer, StochControlSGD, is significantly more robust to large learning rates and can adaptively and individually control the learning rates of the variational parameters. The evolution of the control suggests separate and distinct dynamical behaviours in the training regimes for the mean and uncertainty parameters in Bayesian neural networks. MDPI 2022-08-09 /pmc/articles/PMC9407447/ /pubmed/36010761 http://dx.doi.org/10.3390/e24081097 Text en © 2022 by the authors. https://creativecommons.org/licenses/by/4.0/Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Winkler, Ludwig
Ojeda, César
Opper, Manfred
Stochastic Control for Bayesian Neural Network Training
title Stochastic Control for Bayesian Neural Network Training
title_full Stochastic Control for Bayesian Neural Network Training
title_fullStr Stochastic Control for Bayesian Neural Network Training
title_full_unstemmed Stochastic Control for Bayesian Neural Network Training
title_short Stochastic Control for Bayesian Neural Network Training
title_sort stochastic control for bayesian neural network training
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9407447/
https://www.ncbi.nlm.nih.gov/pubmed/36010761
http://dx.doi.org/10.3390/e24081097
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