MA1: Machine Learning and Stochastic Control

About

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

Target group

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

Advanced Bachelor’s students, Master’s students, PhD students and post-docs

Course aim

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
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