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

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.