Exploiting Symmetry in High-Dimensional Dynamic Programming

主讲人：Jesse Perla（University of British Columbia）

主持人：余昌华（北京大学国家发展研究院）

时间：2022年10月18日（周二）上午10:00-11:30（北京时间）

地点：承泽园246教室

Zoom会议号：926 3889 7210

密码：908060

摘要：We propose a new method for solving high-dimensional dynamic programming problems and recursive competitive equilibria with a large (but finite) number of heterogeneous agents using deep learning. We avoid the curse of dimensionality thanks to three complementary techniques: (1) exploiting symmetry in the approximate law of motion and the value function; (2) constructing a concentration of measure to calculate high-dimensional expectations using a single Monte Carlo draw from the distribution of idiosyncratic shocks; and (3) designing and training deep learning architectures that exploit symmetry and concentration of measure. As an application, we find a global solution of a multi-firm version of the classic Lucas and Prescott (1971) model of investment under uncertainty. First, we compare the solution against a linear-quadratic Gaussian version for validation and benchmarking. Next, we solve the nonlinear version where no accurate or closed-form solution exists. Finally, we describe how our approach applies to a large class of models in economics.

主讲人介绍：Jesse Perla (jesse.perla@ubc.ca) is an associate professor at the Vancouver School of Economics of University of British Columbia. He received his PhD from New York University. His research interests are in Macroeconomics, Machine Learning, Growth, Macro-Development, Bounded Rationality. He has published papers on American Economic Review, Econometrica, Journal of Political Economy and Journal of Economic Growth.