ORIE Colloquium: Ruimeng Hu (Columbia) - Deep Fictitious Play for Stochastic Differential Games

Description

Stochastic differential games can be used to model competitions in Fintech industries, i.e. in P2P lending platforms, insurance markets. Computing Nash equilibria is one of the core objectives in differential games, with a major bottleneck coming from the notorious intractability of N-player games, also known by the curse of dimensionality. To overcome this difficulty, we apply the idea of fictitious play to design deep neural networks (DNNs), and develop deep learning theory and algorithms, for which we refer as deep fictitious play. The resulted deep learning algorithm is scalable, parallelizable and model-free. We illustrate the performance of proposed algorithms by comparing them to the closed-form solution of the linear-quadratic game. We also prove the convergence of the fictitious play under appropriate assumptions and verify that the convergent limit forms an open-loop Nash equilibrium. Based on the formulation by backward stochastic differential equations, we extend the strategy of deep fictitious play to compute closed-loop Markovian Nash equilibrium for both homogeneous and heterogeneous large N-player games.

Bio:
Ruimeng Hu is a term assistant professor in the Department of Statistics at Columbia University. She received her Ph.D. in statistics and applied probability at the University of California, Santa Barbara in 2018. Her research generally lies in the interdisciplinary area of machine learning, financial mathematics, and game theory. She was awarded by the AMS research funds for follow-up MRC collaboration, and finalists of SIAM Conference Paper Prize (SIAG/FME) in both 2016 and 2019.