MATJ5120 MA1: Machine Learning and Stochastic Control (JSS34) (2 cr)

This course explores the interplay between machine learning and stochastic control, addressing some challenges in decision-making under uncertainty.
Plan of the course:
I. Foundations of Machine learning and stochastic control
1. Introduction/motivation
2. Basics of Markov decision process (MDP) and Reinforcement learning (RL)

II. Deep learning for stochastic control and PDEs
1. Neural networks algorithms for MDP
2. Deep Galerkin, Physics-Informed neural networks
3. Deep backward SDE
4. Deep backward dynamic programming

III. Reinforcement learning methods in continuous time
1. Exploratory formulation of RL
2. Policy gradient methods and actor/critic algorithms
3. q-learning and approximation in continuous time   

By the end of the course, participants will be able to:

• Understand Key concepts of stochastic control, deep learning and reinforcement learning, including Bellman equations, value functions, and policy optimization.
• Describe the mathematical and computational connections between ML and stochastic control.
• Apply Machine Learning to Stochastic Control by
  • Formulating real-world problems (e.g., in finance or robotics) as stochastic control or RL tasks.
  • Using machine learning techniques to solve stochastic control problems, including: the resolution of PDEs and BSDEs with neural networks, and the implementation of RL algorithms in continuous and discrete time.  

Usual notions on measures, integration and probability theory, stochastic calculus: Brownian motion, Itô’s formula, Feynman-Kac formula.