Exploiting Symmetry in High-Dimensional Dynamic Programming

Mahdi Ebrahimi Kahou, Jesus Fernandez-Villaverde, Jesse Perla (jesseperla@gmail.com) and Arnav Sood

No 28981, NBER Working Papers from National Bureau of Economic Research, Inc

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. We avoid the curse of dimensionality thanks to three 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; and (3) designing and training deep learning architectures that exploit symmetry and concentration of measure. As an application, we find 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 the nonlinear version where no accurate or closed-form solution exists. Finally, we describe how our approach applies to a large class of models in economics.

JEL-codes: C02 E00 (search for similar items in EconPapers)
Date: 2021-07
New Economics Papers: this item is included in nep-big, nep-mac and nep-ore
Note: EFG
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Citations: View citations in EconPapers (6)

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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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