Machine Learning for High-Dimensional Dynamic Stochastic Economies

Abstract We present a novel computational framework that can compute global solutions to high-dimensional dynamic stochastic economic models on irregular state space geometries. This framework can also resolve value and policy functions’ local features and perform uncertainty quantification, in a single model evaluation. We achieve this by combining Gaussian process machine learning with active subspaces; we then embed this into a parallelized discrete-time dynamic programming algorithm. To demonstrate the broad applicability of our method, we compute solutions to stochastic optimal growth models of up to 500 continuous dimensions. We also show that our framework can address parameter uncertainty and can provide predictive confidence intervals for policies that correspond to the epistemic uncertainty induced by limited data. Finally, we propose an algorithm that, based on combining this framework with Bayesian Gaussian mixture models, is capable of learning irregularly shaped ergodic sets as well as performing dynamic programming on them.