Exploiting Symmetry in High-Dimensional Dynamic Programming

Fernández-Villaverde, Jesús, Mahdi Ebrahimi Kahou, Jesse Perla () and Arnav Sood
Authors registered in the RePEc Author Service: Jesus Fernandez-Villaverde

No 16285, CEPR Discussion Papers from C.E.P.R. Discussion Papers

Abstract: 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.

Keywords: Machine learning; Dynamic programming (search for similar items in EconPapers)
Date: 2021-06
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Working Paper: Exploiting Symmetry in High-Dimensional Dynamic Programming (2021)
Working Paper: Exploiting Symmetry in High-Dimensional Dynamic Programming (2021)
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