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Langevin algorithms for Markovian Neural Networks and Deep Stochastic control

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  • Pierre Bras
  • Gilles Pag`es

Abstract

Stochastic Gradient Descent Langevin Dynamics (SGLD) algorithms, which add noise to the classic gradient descent, are known to improve the training of neural networks in some cases where the neural network is very deep. In this paper we study the possibilities of training acceleration for the numerical resolution of stochastic control problems through gradient descent, where the control is parametrized by a neural network. If the control is applied at many discretization times then solving the stochastic control problem reduces to minimizing the loss of a very deep neural network. We numerically show that Langevin algorithms improve the training on various stochastic control problems like hedging and resource management, and for different choices of gradient descent methods.

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  • Pierre Bras & Gilles Pag`es, 2022. "Langevin algorithms for Markovian Neural Networks and Deep Stochastic control," Papers 2212.12018, arXiv.org, revised Jan 2023.
    • Handle: RePEc:arx:papers:2212.12018
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    References listed on IDEAS

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    1. Stéphane Goutte & Idris Kharroubi & Thomas Lim, 2018. "Optimal management of an oil exploitation," International Journal of Global Energy Issues, Inderscience Enterprises Ltd, vol. 41(1/2/3/4), pages 69-85.
    2. M’hamed Gaïgi & Stéphane Goutte & Idris Kharroubi & Thomas Lim, 2021. "Optimal risk management problem of natural resources: application to oil drilling," Annals of Operations Research, Springer, vol. 297(1), pages 147-166, February.
    3. Achref Bachouch & Côme Huré & Nicolas Langrené & Huyên Pham, 2022. "Deep Neural Networks Algorithms for Stochastic Control Problems on Finite Horizon: Numerical Applications," Methodology and Computing in Applied Probability, Springer, vol. 24(1), pages 143-178, March.
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