Deep Learning Solution to "Combinatorial" Problems in Economics: Analytic and Probabilistic Approaches

Abstract

Many "combinatorial" problems in economics arise from the static or discrete timing assumption that condenses a series of simple binary choices scattered randomly over time into a single instance. Leaning on this insight, we transform combinatorial choices into a sequence of binary choices in continuous time. The complexity of combinatorial choices turns into the dimensionality problem of dynamic optimization, which is overcome by deep learning to a certain degree. Our approaches cover models with both discrete states driven by jump processes and continuous states driven by diffusion processes. To demonstrate the application of deep learning, we consider several examples with high-dimensional states in three areas: international trade, industrial organization, and social network.

Keywords: combinatorial choice, network formation, the curse of dimensionality, backward stochastic differential equation, deep learning

JEL Classification: C63, C67, D85, F23