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  1. Exploiting symmetry in high-dimensional dynamic programming
    Author: Kahou, Mahdi Ebrahimi; Fernández-Villaverde, Jesús; Perla, Jesse; Sood, Arnav
    Published: June 2021
    Publisher:  CESifo, Center for Economic Studies & Ifo Institute, Munich, Germany

    We propose a new method for solving high-dimensional dynamic programming problems and recursive competitive equilibria with a large (but finite) number of heterogeneous agents using deep learning. The "curse of dimensionality" is avoided due to four... more

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    ZBW - Leibniz-Informationszentrum Wirtschaft, Standort Kiel
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    DS 63
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    We propose a new method for solving high-dimensional dynamic programming problems and recursive competitive equilibria with a large (but finite) number of heterogeneous agents using deep learning. The "curse of dimensionality" is avoided due to four complementary techniques: (1) exploiting symmetry in the approximate law of motion and the value function; (2) constructing a concentration of measure to calculate high-dimensional expectations using a single Monte Carlo draw from the distribution of idiosyncratic shocks; (3) sampling methods to ensure the model fits along manifolds of interest; and (4) selecting the most generalizable over-parameterized deep learning approximation without calculating the stationary distribution or applying a transversality condition. As an application, we solve a global solution of a multi-firm version of the classic Lucas and Prescott (1971) model of "investment under uncertainty." First, we compare the solution against a linear-quadratic Gaussian version for validation and benchmarking. Next, we solve nonlinear versions with aggregate shocks. Finally, we describe how our approach applies to a large class of models in economics.

     
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    Source: Union catalogues
    Language: English
    Media type: Book
    Format: Online
    Other identifier:
    hdl: 10419/236703
    Series: CESifo working paper ; no. 9161 (2021)
    Subjects: dynamic programming; deep learning; breaking the curse of dimensionality
    Scope: 1 Online-Ressource (circa 50 Seiten), Illustrationen
  2. Exploiting symmetry in high-dimensional dynamic programming
    Author: Kahou, Mahdi Ebrahimi; Fernández-Villaverde, Jesús; Perla, Jesse; Sood, Arnav
    Published: 23 June 2021
    Publisher:  Centre for Economic Policy Research, London

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    ZBW - Leibniz-Informationszentrum Wirtschaft, Standort Kiel
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    Universitätsbibliothek Mannheim
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    Source: Union catalogues
    Language: English
    Media type: Book
    Format: Online
    Series: Array ; DP16285
    Subjects: Machine Learning; Dynamic programming
    Scope: 1 Online-Ressource (circa 51 Seiten), Illustrationen
  3. Exploiting Symmetry in High-Dimensional Dynamic Programming
    Author: Kahou, Mahdi Ebrahimi; Fernández-Villaverde, Jesús; Perla, Jesse; Sood, Arnav
    Published: 2021
    Publisher:  National Bureau of Economic Research, Cambridge, Mass

    We propose a new method for solving high-dimensional dynamic programming problems and recursive competitive equilibria with a large (but finite) number of heterogeneous agents using deep learning. The "curse of dimensionality" is avoided due to four... more

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    Sächsische Landesbibliothek - Staats- und Universitätsbibliothek Dresden
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    Universitätsbibliothek Freiburg
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    Helmut-Schmidt-Universität, Universität der Bundeswehr Hamburg, Universitätsbibliothek
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    Staats- und Universitätsbibliothek Hamburg Carl von Ossietzky
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    Technische Informationsbibliothek (TIB) / Leibniz-Informationszentrum Technik und Naturwissenschaften und Universitätsbibliothek
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    ZBW - Leibniz-Informationszentrum Wirtschaft, Standort Kiel
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    We propose a new method for solving high-dimensional dynamic programming problems and recursive competitive equilibria with a large (but finite) number of heterogeneous agents using deep learning. The "curse of dimensionality" is avoided due to four complementary techniques: (1) exploiting symmetry in the approximate law of motion and the value function; (2) constructing a concentration of measure to calculate high-dimensional expectations using a single Monte Carlo draw from the distribution of idiosyncratic shocks; (3) sampling methods to ensure the model fits along manifolds of interest; and (4) selecting the most generalizable over-parameterized deep learning approximation without calculating the stationary distribution or applying a transversality condition. As an application, we solve a global solution of a multi-firm version of the classic Lucas and Prescott (1971) model of "investment under uncertainty." First, we compare the solution against a linear-quadratic Gaussian version for validation and benchmarking. Next, we solve nonlinear versions with aggregate shocks. Finally, we describe how our approach applies to a large class of models in economics

     
    Export to reference management software   RIS file
      BibTeX file
    Source: Union catalogues
    Language: English
    Media type: Book
    Format: Online
    Other identifier:
    Series: NBER working paper series ; no. w28981
    Subjects: Dynamische Optimierung; Monte-Carlo-Simulation; Theorie
    Scope: 1 Online-Ressource, illustrations (black and white)
    Notes:

    Hardcopy version available to institutional subscribers