| Résumé | 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
Carlo. |
