Artificial neural networks to solve dynamic programming problems: A bias-corrected Monte Carlo operator

Julien Pascal

Journal of Economic Dynamics and Control, 2024, vol. 162, issue C

Abstract: Artificial Neural Networks (ANNs) are powerful tools that can solve dynamic programming problems arising in economics. In this context, estimating ANN parameters involves minimizing a loss function based on the model's stochastic functional equations. In general, the expectations appearing in the loss function admit no closed-form solution, so numerical approximation techniques must be used. In this paper, I analyze a bias-corrected Monte Carlo operator (bc-MC) that approximates expectations by Monte Carlo. I show that the bc-MC operator is a generalization of the all-in-one expectation operator, already proposed in the literature. I demonstrate that, under some conditions on the primitives of the economic model, the bc-MC operator is the unbiased estimator of the loss function with the minimum variance. I propose a method to optimally set the hyperparameters defining the bc-MC operator, and illustrate the findings numerically with well-known economic models. I also demonstrate that the bc-MC operator can scale to high-dimensional models. With just approximately a minute of computing time, I find a global solution to an economic model with a kink in the decision function and more than 100 dimensions.

Keywords: Dynamic programming; Artificial neural network; Machine learning; Monte Carlo (search for similar items in EconPapers)
JEL-codes: C45 C61 C63 C68 E32 E37 (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Working Paper: Artificial neural networks to solve dynamic programming problems: A bias-corrected Monte Carlo operator (2023)
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Persistent link: https://EconPapers.repec.org/RePEc:eee:dyncon:v:162:y:2024:i:c:s0165188924000459

DOI: 10.1016/j.jedc.2024.104853

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