Artificial Neural Networks to solve dynamic programming problems: a bias-corrected Monte Carlo operator

DateMarch 2023
AuteurJulien Pascal

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 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 a few minutes
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

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