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...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2022-08-01
|
| Series: | Entropy |
| Subjects: | |
| Online Access: | https://www.mdpi.com/1099-4300/24/8/1097 |
| _version_ | 1797445606752387072 |
|---|---|
| author | Ludwig Winkler César Ojeda Manfred Opper |
| author_facet | Ludwig Winkler César Ojeda Manfred Opper |
| author_sort | Ludwig Winkler |
| collection | DOAJ |
| 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. |
| first_indexed | 2024-03-09T13:29:19Z |
| format | Article |
| id | doaj.art-7d7273ff5d5b4a14902a25c51007f2d9 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-09T13:29:19Z |
| publishDate | 2022-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-7d7273ff5d5b4a14902a25c51007f2d92023-11-30T21:20:28ZengMDPI AGEntropy1099-43002022-08-01248109710.3390/e24081097Stochastic Control for Bayesian Neural Network TrainingLudwig Winkler0César Ojeda1Manfred Opper2Machine Learning Group, Technische Universität Berlin, 10623 Berlin, GermanyArtificial Intelligence Group, Technische Universität Berlin, 10623 Berlin, GermanyArtificial Intelligence Group, Technische Universität Berlin, 10623 Berlin, GermanyIn 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.https://www.mdpi.com/1099-4300/24/8/1097Bayesian inferenceBayesian neural networkslearning |
| spellingShingle | Ludwig Winkler César Ojeda Manfred Opper Stochastic Control for Bayesian Neural Network Training Entropy Bayesian inference Bayesian neural networks learning |
| 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 | Bayesian inference Bayesian neural networks learning |
| url | https://www.mdpi.com/1099-4300/24/8/1097 |
| work_keys_str_mv | AT ludwigwinkler stochasticcontrolforbayesianneuralnetworktraining AT cesarojeda stochasticcontrolforbayesianneuralnetworktraining AT manfredopper stochasticcontrolforbayesianneuralnetworktraining |