Abstract: In this talk, we discuss the feasibility of algorithms based on deep neural networks (DNNs) for solving high-dimensional stochastic control problems. These problems seek optimal control of stochastic differential equations driven by a vast number of risk factors, and are crucial for numerous applications including production planning, crowd control, asset allocation and risk management. We first show that in certain cases, DNNs can break the curse of dimensionality in representing high-dimensional value functions of stochastic control problems. We then introduce several provably convergent neural network based algorithms to solve stochastic control problems, stochastic games, and mean-field control problems. Finally, we shall discuss how stochastic control theory helps provide a theoretical justification for recent reinforcement learning heuristics.

Bio: I am a final year DPhil student in Mathematical and Computational Finance Group at the University of Oxford, supervised by Prof. Christoph Reisinger. My research interests lie at the intersection of stochastic control and games, machine learning and mathematical finance.