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Deep neural networks algorithms for stochastic control problems on finite horizon: numerical applications

Author

Listed:
  • Achref Bachouch

    (UiO - University of Oslo)

  • Côme Huré

    (LPSM (UMR_8001) - Laboratoire de Probabilités, Statistique et Modélisation - UPD7 - Université Paris Diderot - Paris 7 - SU - Sorbonne Université - CNRS - Centre National de la Recherche Scientifique)

  • Nicolas Langrené

    (CSIRO - Data61 [Canberra] - ANU - Australian National University - CSIRO - Commonwealth Scientific and Industrial Research Organisation [Canberra])

  • Huyen Pham

    (LPSM (UMR_8001) - Laboratoire de Probabilités, Statistique et Modélisation - UPD7 - Université Paris Diderot - Paris 7 - SU - Sorbonne Université - CNRS - Centre National de la Recherche Scientifique)

Abstract

This paper presents several numerical applications of deep learning-based algorithms that have been introduced in [HPBL18]. Numerical and comparative tests using TensorFlow illustrate the performance of our different algorithms, namely control learning by performance iteration (algorithms NNcontPI and ClassifPI), control learning by hybrid iteration (algorithms Hybrid-Now and Hybrid-LaterQ), on the 100-dimensional nonlinear PDEs examples from [EHJ17] and on quadratic backward stochastic differential equations as in [CR16]. We also performed tests on low-dimension control problems such as an option hedging problem in finance, as well as energy storage problems arising in the valuation of gas storage and in microgrid management. Numerical results and comparisons to quantization-type algorithms Qknn, as an efficient algorithm to numerically solve low-dimensional control problems, are also provided; and some corresponding codes are available on https://github.com/comeh/.

Suggested Citation

  • Achref Bachouch & Côme Huré & Nicolas Langrené & Huyen Pham, 2020. "Deep neural networks algorithms for stochastic control problems on finite horizon: numerical applications," Post-Print hal-01949221, HAL.
    • Handle: RePEc:hal:journl:hal-01949221
    Note: View the original document on HAL open archive server: https://hal.science/hal-01949221v3
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    References listed on IDEAS

    as
    1. Daniel R. Jiang & Warren B. Powell, 2015. "An Approximate Dynamic Programming Algorithm for Monotone Value Functions," Operations Research, INFORMS, vol. 63(6), pages 1489-1511, December.
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    Cited by:

    1. Nicolas Curin & Michael Kettler & Xi Kleisinger-Yu & Vlatka Komaric & Thomas Krabichler & Josef Teichmann & Hanna Wutte, 2021. "A deep learning model for gas storage optimization," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 44(2), pages 1021-1037, December.

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    More about this item

    Keywords

    reinforcement learning; Policy iteration algorithm; Deep learning; value iteration; quantization;
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