Abstract: We prove that a single-layer neural network trained with the Q-learning algorithm converges in distribution to a random ordinary differential equation as the size of the model and the number of training steps become large. Analysis of the limit differential equation shows that it has a unique stationary solution which is the solution of the Bellman equation, thus giving the optimal control for the problem. In addition, we study the convergence of the limit differential equation to the stationary solution. In the second part of the presentation, we will discuss applications of reinforcement learning to optimal execution of orders in quantitative finance.

Bio: Justin Sirignano is Associate Professor of Mathematics at the Oxford Mathematical Institute and Director of the Oxford Masters program in Mathematical & Computational Finance. Justin's research lies at the intersection of applied mathematics, machine learning, and high-performance computing and is focused on theory and applications of Deep Learning. Justin received his PhD from Stanford University and holds a Bachelor's degree from Princeton University. He was awarded the 2014 SIAM Financial Mathematics and Engineering Conference Paper Prize.